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:

300 = 2 * p i * r^{2} + 2 * p i * r * 12 - 6.2831853071796 r^{2} - 75.398 r + 300 = 0 6.2831853071796 r^{2} + 75.398 r - 300 = 0 a = 6.283185; b = 75.398; c = - 300 D = b^{2} - 4 a c = 75.39 8^{2} - 4 \cdot 6.283185 \cdot (- 300) = 13224.714503643 D > 0 r_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 7 5 . 4 \pm 1 3 2 2 4 . 7 1}{1 2 . 5 6 6 3 7 1} r_{1, 2} = - 6 \pm 9.15131 r_{1} = 3.151310449 r_{2} = - 15.151310449 Factored form of the equation: 6.2831853071796 (r - 3.151310449) (r + 15.151310449) = 0

Solution in text:

-6.2831853071796r²-75.398223686155r+300=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 13224.714503643
D > 0 ... The equation has two distinct real roots

r₁ = 3.1513104
r₂ = -15.1513104

P = {3.1513104; -15.1513104}