Quadratic Formula calculator

$a{x}^2+\mathrm{bx}+\mathrm{c}=0$

a

b

c

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Calculator use

This quadratic equation calculator is a powerful tool for solving second-order polynomials such as $a{x}^2+\mathrm{bx}+\mathrm{c}=0$. With its user-friendly interface and precise results, it's the perfect solution for finding x when a ≠ 0.

Get Accurate Results with Our Quadratic Equation Calculator: Find Real and Complex Roots Effortlessly. The solution process will be displayed step-by-step using the quadratic formula. The calculator also determines the discriminant ($b^2$-4ac ) and its relationship to zero

Quadratic Formula

x = $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Quadratic Formula Made Easy: Step-by-Step Examples for Better Understanding

Example 1

Solve the equation $5x^2-\mathrm{2x}-1=0$

a = 5, b = -2, c = -1

x = $\frac{-\mathrm{(-2)}\pm \sqrt{{\mathrm{(-2)}}^2-4\mathrm{\times 5}\mathrm{\times -1}}}{2\mathrm{\times 5}}$

x = $\frac{2\pm \sqrt{4-\mathrm{(-20)}}}{10}$

x = $\frac{2\pm \sqrt{4+20}}{10}$

x = $\frac{2\pm \sqrt{\mathrm{24}}}{10}$

x = $\frac{2\pm \mathrm{4.899}}{10}$

x = $\frac{2+\mathrm{4.899}}{10}$ and $\frac{2-\mathrm{4.899}}{10}$

Answer: x = 0.69 and x = -0.29

Example 2

Solve the equation $2x^2+\mathrm{3x}-7$ ,giving your answers to 2 decimal places

a = 2, b = 3, c = - 7

$\frac{-3\pm \sqrt{\left(3^2\right)-(4\times 2\times \mathrm{-7})}}{2\times 2}$

$\frac{-3\pm \sqrt{\left(9\right)-(-56)}}{4}$

$\frac{-3\pm \sqrt{9+56}}{4}$

$\frac{-3\pm \sqrt{65}}{4}$

x = $\frac{-3+\sqrt{65}}{4}$ or x = $\frac{-3-\sqrt{65}}{4}$

Answer: x = -2.77 or x = 1.27