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:

24 = a * (10 - a) a^{2} - 10 a + 24 = 0 p = 1; q = - 10; r = 24 D = q^{2} - 4 p r = 1 0^{2} - 4 \cdot 1 \cdot 24 = 4 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{1 0 \pm 4}{2} a_{1, 2} = \frac{1 0 \pm 2}{2} a_{1, 2} = 5 \pm 1 a_{1} = 6 a_{2} = 4 Factored form of the equation: (a - 6) (a - 4) = 0

Solution in text:

a²-10a+24=0 ... quadratic equation

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

a₁ = 6
a₂ = 4

P = {6; 4}