x^2+14x+31=-5

Solution for x^2+14x+31=-5 equation:

x^2+14x+31=-5

We move all terms to the left:

x^2+14x+31-(-5)=0

We add all the numbers together, and all the variables

x^2+14x+36=0

a = 1; b = 14; c = +36;
Δ = b2-4ac
Δ = 142-4·1·36
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{13}}{2*1}=\frac{-14-2\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{13}}{2*1}=\frac{-14+2\sqrt{13}}{2}
$