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:

j * (j - 3) = 180 j^{2} - 3 j - 180 = 0 a = 1; b = - 3; c = - 180 D = b^{2} - 4 a c = 3^{2} - 4 \cdot 1 \cdot (- 180) = 729 D > 0 j_{1, 2} = \frac{- b \pm D}{2 a} = \frac{3 \pm 7 2 9}{2} j_{1, 2} = \frac{3 \pm 2 7}{2} j_{1, 2} = 1.5 \pm 13.5 j_{1} = 15 j_{2} = - 12 Factored form of the equation: (j - 15) (j + 12) = 0

Solution in text:

j²-3j-180=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 729
D > 0 ... The equation has two distinct real roots

j₁ = 15
j₂ = -12

P = {15; -12}