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:

9 r^{2} + 27 r + 27 = 819.3296 9 r^{2} + 27 r - 792.33 = 0 a = 9; b = 27; c = - 792.33 D = b^{2} - 4 a c = 2 7^{2} - 4 \cdot 9 \cdot (- 792.33) = 29252.8656 D > 0 r_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 2 7 \pm 2 9 2 5 2 . 8 7}{1 8} r_{1, 2} = - 1.5 \pm 9.501927 r_{1} = 8.00192729 r_{2} = - 11.00192729 Factored form of the equation: 9 (r - 8.00192729) (r + 11.00192729) = 0

Solution in text:

9r²+27r-792.3296=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 29252.8656
D > 0 ... The equation has two distinct real roots

r₁ = 8.0019273
r₂ = -11.0019273

P = {8.0019273; -11.0019273}