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:

70 = a (a - 3) - a^{2} + 3 a + 70 = 0 a^{2} - 3 a - 70 = 0 p = 1; q = - 3; r = - 70 D = q^{2} - 4 p r = 3^{2} - 4 \cdot 1 \cdot (- 70) = 289 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{3 \pm 2 8 9}{2} a_{1, 2} = \frac{3 \pm 1 7}{2} a_{1, 2} = 1.5 \pm 8.5 a_{1} = 10 a_{2} = - 7 Factored form of the equation: (a - 10) (a + 7) = 0

Solution in text:

-a²+3a+70=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 289
D > 0 ... The equation has two distinct real roots

a₁ = 10
a₂ = -7

P = {10; -7}