X^2-5+18x+31=180

Solution for X^2-5+18x+31=180 equation:

X^2-5+18X+31=180

We move all terms to the left:

X^2-5+18X+31-(180)=0

We add all the numbers together, and all the variables

X^2+18X-154=0

a = 1; b = 18; c = -154;
Δ = b2-4ac
Δ = 182-4·1·(-154)
Δ = 940
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:

$\sqrt{\Delta}=\sqrt{940}=\sqrt{4*235}=\sqrt{4}*\sqrt{235}=2\sqrt{235}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{235}}{2*1}=\frac{-18-2\sqrt{235}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{235}}{2*1}=\frac{-18+2\sqrt{235}}{2}
$