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:

500 4^{2} = 260 0^{2} + c^{2} - 2 * 2600 * c * 0.59130964836358 - c^{2} + 3074.81 c + 18280016 = 0 c^{2} - 3074.81 c - 18280016 = 0 p = 1; q = - 3074.81; r = - 18280016 D = q^{2} - 4 p r = 3074.8 1^{2} - 4 \cdot 1 \cdot (- 18280016) = 82574521.590713 D > 0 c_{1, 2} = \frac{- q \pm D}{2 p} = \frac{3 0 7 4 . 8 1 \pm 8 2 5 7 4 5 2 1 . 5 9}{2} c_{1, 2} = 1537.405086 \pm 4543.526207 c_{1} = 6080.931293184 c_{2} = - 3006.121121692 Factored form of the equation: (c - 6080.931293184) (c + 3006.121121692) = 0

Solution in text:

-c²+3074.8101714924c+18280016=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 82574521.590713
D > 0 ... The equation has two distinct real roots

c₁ = 6080.9312932
c₂ = -3006.1211217

P = {6080.9312932; -3006.1211217}