x^2-11x-31=0

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

x^2-11x-31=0

a = 1; b = -11; c = -31;
Δ = b2-4ac
Δ = -112-4·1·(-31)
Δ = 245
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{245}=\sqrt{49*5}=\sqrt{49}*\sqrt{5}=7\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-7\sqrt{5}}{2*1}=\frac{11-7\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+7\sqrt{5}}{2*1}=\frac{11+7\sqrt{5}}{2}
$