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

a

b

c

## Calculator use

This quadratic equation calculator is a powerful tool for solving second-order polynomials such as $a{x}^{2}+bx+c=0$. 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

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

#### Example 1

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

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

x = $\frac{-\mathrm{\left(-2\right)}±\sqrt{{\mathrm{\left(-2\right)}}^{2}-4\mathrm{×5}\mathrm{×-1}}}{2\mathrm{×5}}$

x = $\frac{2±\sqrt{4-\left(-20\right)}}{10}$

x = $\frac{2±\sqrt{4+20}}{10}$

x = $\frac{2±\sqrt{\mathrm{24}}}{10}$

x = $\frac{2±\mathrm{4.899}}{10}$

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 $2{x}^{2}+3x-7$ ,giving your answers to 2 decimal places

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

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

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

$\frac{-3±\sqrt{9+56}}{4}$

$\frac{-3±\sqrt{65}}{4}$

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

Answer: x = -2.77 or x = 1.27