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:

4 x^{2} - 5 x + 34 = x (x - 2) 3 x^{2} - 3 x + 34 = 0 a = 3; b = - 3; c = 34 D = b^{2} - 4 a c = 3^{2} - 4 \cdot 3 \cdot 34 = - 399 D < 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{3 \pm - 3 9 9}{6} x_{1, 2} = \frac{3 \pm i 3 9 9}{6} x_{1, 2} = 0.5 \pm 3.329164 i x_{1} = 0.5 + 3.3291640592397 i x_{2} = 0.5 - 3.3291640592397 i Factored form of the equation: 3 (x - 0.5 - 3.3291640592397 i) (x - 0.5 + 3.3291640592397 i) = 0

Solution in text:

3x²-3x+34=0 ... quadratic equation

Discriminant:
D = b² - 4ac = -399
D < 0 ... The equation has two distinct complex roots

x₁ = 0.5+3.3291641i
x₂ = 0.5-3.3291641i

P = {0.5+3.3291641i; 0.5-3.3291641i}