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:

5^{2} = (2 + z)^{2} + (z / 2)^{2} - 1.25 z^{2} - 4 z + 21 = 0 1.25 z^{2} + 4 z - 21 = 0 a = 1.25; b = 4; c = - 21 D = b^{2} - 4 a c = 4^{2} - 4 \cdot 1.25 \cdot (- 21) = 121 D > 0 z_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 4 \pm 1 2 1}{2 . 5} z_{1, 2} = \frac{- 4 \pm 1 1}{2 . 5} z_{1, 2} = - 1.6 \pm 4.4 z_{1} = 2.8 z_{2} = - 6 Factored form of the equation: 1.25 (z - 2.8) (z + 6) = 0

Solution in text:

-1.25z²-4z+21=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 121
D > 0 ... The equation has two distinct real roots

z₁ = 2.8
z₂ = -6

P = {2.8; -6}