Quadratic equation calculator

Quadratic equation has the basic form:

a x^{2} + b x + c = 0

Enter the coefficients a, b, c of quadratic equation in 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:

140 = 3 * s q r t (3) * a^{2} + 30 a - 5.19615242271 a^{2} - 30 a + 140 = 0 5.19615242271 a^{2} + 30 a - 140 = 0 p = 5.19615242271; q = 30; r = - 140 D = q^{2} - 4 p r = 3 0^{2} - 4 \cdot 5.19615242271 \cdot (- 140) = 3809.84535672 D > 0 a_{1, 2} = \frac{- q \pm \sqrt{D}}{2 p} = \frac{- 30 \pm \sqrt{3809.85}}{10.3923048454} a_{1, 2} = - 2.88675135 \pm 5.93938935376 a_{1} = 3.05263800781 a_{2} = - 8.8261406997 Factored form of the equation: 5.19615242271 (a - 3.05263800781) (a + 8.8261406997) = 0

Solution in text:

-5.19615242271a²-30a+140=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 3809.84535672
D>0 ... The equation has two distinct real roots

a₁ = 3.05263800781
a₂ = -8.8261406997

P = {3.05263800781; -8.8261406997}