11x^2-31x-4=0

Solution for 11x^2-31x-4=0 equation:

11x^2-31x-4=0

a = 11; b = -31; c = -4;
Δ = b2-4ac
Δ = -312-4·11·(-4)
Δ = 1137
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-\sqrt{1137}}{2*11}=\frac{31-\sqrt{1137}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{1137}}{2*11}=\frac{31+\sqrt{1137}}{22}
$