X^2+22x+5=-31

Solution for X^2+22x+5=-31 equation:

X^2+22X+5=-31

We move all terms to the left:

X^2+22X+5-(-31)=0

We add all the numbers together, and all the variables

X^2+22X+36=0

a = 1; b = 22; c = +36;
Δ = b2-4ac
Δ = 222-4·1·36
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{85}}{2*1}=\frac{-22-2\sqrt{85}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{85}}{2*1}=\frac{-22+2\sqrt{85}}{2}
$