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:

a (34 / 2 - a) = 70 - a^{2} + 17 a - 70 = 0 a^{2} - 17 a + 70 = 0 p = 1; q = - 17; r = 70 D = q^{2} - 4 p r = 1 7^{2} - 4 \cdot 1 \cdot 70 = 9 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{1 7 \pm 9}{2} a_{1, 2} = \frac{1 7 \pm 3}{2} a_{1, 2} = 8.5 \pm 1.5 a_{1} = 10 a_{2} = 7 Factored form of the equation: (a - 10) (a - 7) = 0

Solution in text:

-a²+17a-70=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 9
D > 0 ... The equation has two distinct real roots

a₁ = 10
a₂ = 7

P = {10; 7}