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:

a * (130 - 2 a) = 2 * 800.25 - 2 a^{2} + 130 a - 1600.5 = 0 2 a^{2} - 130 a + 1600.5 = 0 p = 2; q = - 130; r = 1600.5 D = q^{2} - 4 p r = 13 0^{2} - 4 \cdot 2 \cdot 1600.5 = 4096 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{1 3 0 \pm 4 0 9 6}{4} a_{1, 2} = \frac{1 3 0 \pm 6 4}{4} a_{1, 2} = 32.5 \pm 16 a_{1} = 48.5 a_{2} = 16.5 Factored form of the equation: 2 (a - 48.5) (a - 16.5) = 0

Solution in text:

-2a²+130a-1600.5=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 4096
D > 0 ... The equation has two distinct real roots

a₁ = 48.5
a₂ = 16.5

P = {48.5; 16.5}