x^2+18x-31=0

Solution for x^2+18x-31=0 equation:

x^2+18x-31=0

a = 1; b = 18; c = -31;
Δ = b2-4ac
Δ = 182-4·1·(-31)
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-8\sqrt{7}}{2*1}=\frac{-18-8\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+8\sqrt{7}}{2*1}=\frac{-18+8\sqrt{7}}{2}
$