Quadratic Equation Calculator

A quadratic equation has the basic form:

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

Enter the coefficients a, b, and c of the quadratic equation in its basic standardized form. The solution of a quadratic equation usually consists of two distinct real or complex roots, or one double root — calculated using the discriminant.

Calculation:

(5 - d) * (10 + d) = 6 * 6 - d^{2} - 5 d + 14 = 0 d^{2} + 5 d - 14 = 0 a = 1; b = 5; c = - 14 D = b^{2} - 4 a c = 5^{2} - 4 \cdot 1 \cdot (- 14) = 81 D > 0 d_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 5 \pm 8 1}{2} d_{1, 2} = \frac{- 5 \pm 9}{2} d_{1, 2} = - 2.5 \pm 4.5 d_{1} = 2 d_{2} = - 7 Factored form of the equation: (d - 2) (d + 7) = 0

Solution in text:

-d²-5d+14=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 81
D > 0 ... The equation has two distinct real roots

d₁ = 2
d₂ = -7

P = {2; -7}