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:

10 + a + a = 1 / 12 * (10 + a) * a - 0.083333333333332 a^{2} + 1.167 a + 10 = 0 0.083333333333332 a^{2} - 1.167 a - 10 = 0 p = 0.083333; q = - 1.167; r = - 10 D = q^{2} - 4 p r = 1.16 7^{2} - 4 \cdot 0.083333 \cdot (- 10) = 4.6944444444 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{1 . 1 7 \pm 4 . 6 9}{0 . 1 6 6 6 6 7} a_{1, 2} = 7 \pm 13 a_{1} = 20 a_{2} = - 6 Factored form of the equation: 0.083333333333332 (a - 20) (a + 6) = 0

Solution in text:

-0.083333333333332a²+1.1666666666667a+10=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 4.6944444444
D > 0 ... The equation has two distinct real roots

a₁ = 20
a₂ = -6

P = {20; -6}