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:

120 * ((a + 20 * 5) + a) = a * (a + 20 * 5) - a^{2} + 140 a + 12000 = 0 a^{2} - 140 a - 12000 = 0 p = 1; q = - 140; r = - 12000 D = q^{2} - 4 p r = 14 0^{2} - 4 \cdot 1 \cdot (- 12000) = 67600 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{1 4 0 \pm 6 7 6 0 0}{2} a_{1, 2} = \frac{1 4 0 \pm 2 6 0}{2} a_{1, 2} = 70 \pm 130 a_{1} = 200 a_{2} = - 60 Factored form of the equation: (a - 200) (a + 60) = 0

Solution in text:

-a²+140a+12000=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 67600
D > 0 ... The equation has two distinct real roots

a₁ = 200
a₂ = -60

P = {200; -60}