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:

c^{2} = (c - 9)^{2} + (c - 8)^{2} - c^{2} + 34 c - 145 = 0 c^{2} - 34 c + 145 = 0 p = 1; q = - 34; r = 145 D = q^{2} - 4 p r = 3 4^{2} - 4 \cdot 1 \cdot 145 = 576 D > 0 c_{1, 2} = \frac{- q \pm D}{2 p} = \frac{3 4 \pm 5 7 6}{2} c_{1, 2} = \frac{3 4 \pm 2 4}{2} c_{1, 2} = 17 \pm 12 c_{1} = 29 c_{2} = 5 Factored form of the equation: (c - 29) (c - 5) = 0

Solution in text:

-c²+34c-145=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 576
D > 0 ... The equation has two distinct real roots

c₁ = 29
c₂ = 5

P = {29; 5}