Quadratic Equation Calculator

A quadratic equation has the basic form:

a x^{2} + b x + c = 0

Enter the coefficients a, b, and c of the quadratic equation in its basic standardized form. The solution of a quadratic equation usually consists of two distinct real or complex roots, or one double root — calculated using the discriminant.

Calculation:

48 + 24 (c + 1) + 12 (c + 1)^{2} = 76 (c + 1) 12 c^{2} - 28 c + 8 = 0 12 = 2^{2} \cdot 3 28 = 2^{2} \cdot 7 8 = 2^{3} GCD (12, 28, 8) = 2^{2} = 4 3 c^{2} - 7 c + 2 = 0 p = 3; q = - 7; r = 2 D = q^{2} - 4 p r = 7^{2} - 4 \cdot 3 \cdot 2 = 25 D > 0 c_{1, 2} = \frac{- q \pm D}{2 p} = \frac{7 \pm 2 5}{6} c_{1, 2} = \frac{7 \pm 5}{6} c_{1, 2} = 1.166667 \pm 0.833333 c_{1} = 2 c_{2} = 0.333333333 Factored form of the equation: 3 (c - 2) (c - 0.333333333) = 0

Solution in text:

12c²-28c+8=0 ... quadratic equation

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

c₁ = 2
c₂ = 0.3333333

P = {2; 0.3333333}