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 * (0.72 - a) = 0.072 - a^{2} + 0.72 a - 0.072 = 0 a^{2} - 0.72 a + 0.072 = 0 p = 1; q = - 0.72; r = 0.072 D = q^{2} - 4 p r = 0.7 2^{2} - 4 \cdot 1 \cdot 0.072 = 0.2304 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{0 . 7 2 \pm 0 . 2 3}{2} a_{1, 2} = 0.36 \pm 0.24 a_{1} = 0.6 a_{2} = 0.12 Factored form of the equation: (a - 0.6) (a - 0.12) = 0

Solution in text:

-a²+0.72a-0.072=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 0.2304
D > 0 ... The equation has two distinct real roots

a₁ = 0.6
a₂ = 0.12

P = {0.6; 0.12}