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:

4 * ((18 - a) + a) = a (18 - a) a^{2} - 18 a + 72 = 0 p = 1; q = - 18; r = 72 D = q^{2} - 4 p r = 1 8^{2} - 4 \cdot 1 \cdot 72 = 36 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{1 8 \pm 3 6}{2} a_{1, 2} = \frac{1 8 \pm 6}{2} a_{1, 2} = 9 \pm 3 a_{1} = 12 a_{2} = 6 Factored form of the equation: (a - 12) (a - 6) = 0

Solution in text:

a²-18a+72=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 36
D > 0 ... The equation has two distinct real roots

a₁ = 12
a₂ = 6

P = {12; 6}