সমীকরণ সমাধানকারী

How to solve an equation

1. Write the equation. For example 2x^2-5x-3=0 or 3(x-2)=9. A power is written with a caret.
2. Use the ready-made examples. Tap an example to see how the equation is written.
3. Solve. You get the solutions, and for second-degree equations also the discriminant and the steps.

প্রথম ও দ্বিতীয় মাত্রার সমীকরণ

A first-degree equation has the form ax + b = 0, and its solution is x = −b/a. A second-degree equation ax² + bx + c = 0 is solved with the quadratic formula, where the discriminant D = b² − 4ac tells the number of solutions. If D > 0, there are two solutions; if D = 0, one double solution; and if D < 0, there are no real solutions.

Entä monimutkaisemmat yhtälöt?

If the equation contains, for example, trigonometric functions, roots or higher powers, the solver searches for the solutions numerically over a certain interval. This means it finds the points where both sides of the equation are equal. The numerical method is efficient, but it can only find the solutions within the examined interval, so very large or periodic solutions should be checked separately.

Example: a second-degree equation step by step

Let's solve 2x² − 5x − 3 = 0 with the quadratic formula. The coefficients are a = 2, b = −5, c = −3. The discriminant D = b² − 4ac = (−5)² − 4·2·(−3) = 25 + 24 = 49. Since D > 0, there are two solutions. The square root √49 = 7. The formula gives x = (5 ± 7) / 4. So x₁ = 12/4 = 3 and x₂ = −2/4 = −0.5. The calculator shows these steps and the final result automatically.

Sanallisesta tehtävästä yhtälöksi

Many equations arise from a word problem. For example, "a number and its square total 12" translates into x + x² = 12, i.e. x² + x − 12 = 0. Once you identify what the unknown is and write the condition as an equation, solving is straightforward. Remember to check whether both solutions make sense in the situation: for example, a length cannot be negative, so a negative root is often rejected in practical problems.

Equation, inequality and identity

An equation asserts that two expressions are equal, and it is solved by finding the values of the unknown that make the assertion true. Not all equations are alike, however. An identity is an equation that holds for all values of the variable, such as (a+b)² = a² + 2ab + b². A conditional equation, on the other hand, holds only for certain values, such as 2x + 1 = 7 only for x = 3.

An inequality, in turn, compares magnitudes with the signs <, >, ≤ or ≥, and its solution is often a range of numbers rather than a single value. Inequalities are handled largely like equations, but with one important difference: when both sides are multiplied or divided by a negative number, the inequality sign flips. This calculator focuses on equations, but the same simplification principles also help with inequalities.

সংক্ষেপে

The equation solver solves first- and second-degree equations exactly and others numerically. Write the equation with the unknown x and read the solutions, plus for second-degree equations the discriminant and the steps. By moving the terms to the same side you get the equation into a clear form that the tool solves reliably.

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