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:

p o w (1.23, 2) + p o w (1.23 + d, 2) = p o w (1.23 + 2 * d, 2) - 3 d^{2} - 2.46 d + 1.513 = 0 3 d^{2} + 2.46 d - 1.513 = 0 a = 3; b = 2.46; c = - 1.513 D = b^{2} - 4 a c = 2.4 6^{2} - 4 \cdot 3 \cdot (- 1.513) = 24.2064 D > 0 d_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 2 . 4 6 \pm 2 4 . 2 1}{6} d_{1, 2} = - 0.41 \pm 0.82 d_{1} = 0.41 d_{2} = - 1.23 Factored form of the equation: 3 (d - 0.41) (d + 1.23) = 0

Solution in text:

-3d²-2.46d+1.5129=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 24.2064
D > 0 ... The equation has two distinct real roots

d₁ = 0.41
d₂ = -1.23

P = {0.41; -1.23}