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:

300 = a * (80 / 2 - a) a^{2} - 40 a + 300 = 0 p = 1; q = - 40; r = 300 D = q^{2} - 4 p r = 4 0^{2} - 4 \cdot 1 \cdot 300 = 400 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{4 0 \pm 4 0 0}{2} a_{1, 2} = \frac{4 0 \pm 2 0}{2} a_{1, 2} = 20 \pm 10 a_{1} = 30 a_{2} = 10 Factored form of the equation: (a - 30) (a - 10) = 0

Solution in text:

a²-40a+300=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 400
D > 0 ... The equation has two distinct real roots

a₁ = 30
a₂ = 10

P = {30; 10}