Quadratic equation calculator

Quadratic equation has the basic form:

a x^{2} + b x + c = 0

Enter the quadratic equation's coefficients a, b, and c of its basic standardized form. A solution of quadratic equations is usually two different real or complex roots or one double root — the calculation using the discriminant.

Calculation:

- 3 x^{2} - 2 * 41 * x + 41 * 41 = 0 - 3 x^{2} - 82 x + 1681 = 0 3 x^{2} + 82 x - 1681 = 0 a = 3; b = 82; c = - 1681 D = b^{2} - 4 a c = 8 2^{2} - 4 \cdot 3 \cdot (- 1681) = 26896 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 8 2 \pm 2 6 8 9 6}{6} x_{1, 2} = \frac{- 8 2 \pm 1 6 4}{6} x_{1, 2} = - 13.666667 \pm 27.333333 x_{1} = 13.666666667 x_{2} = - 41 Factored form of the equation: 3 (x - 13.666666667) (x + 41) = 0

Solution in text:

-3x²-82x+1681=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 26896
D > 0 ... The equation has two distinct real roots

x₁ = 13.6666667
x₂ = -41

P = {13.6666667; -41}