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:

35 * (a + 24 + a) = a * (a + 24) - a^{2} + 46 a + 840 = 0 a^{2} - 46 a - 840 = 0 p = 1; q = - 46; r = - 840 D = q^{2} - 4 p r = 4 6^{2} - 4 \cdot 1 \cdot (- 840) = 5476 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{4 6 \pm 5 4 7 6}{2} a_{1, 2} = \frac{4 6 \pm 7 4}{2} a_{1, 2} = 23 \pm 37 a_{1} = 60 a_{2} = - 14 Factored form of the equation: (a - 60) (a + 14) = 0

Solution in text:

-a²+46a+840=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 5476
D > 0 ... The equation has two distinct real roots

a₁ = 60
a₂ = -14

P = {60; -14}