x^2-18x+71=-8

Solution for x^2-18x+71=-8 equation:

x^2-18x+71=-8

We move all terms to the left:

x^2-18x+71-(-8)=0

We add all the numbers together, and all the variables

x^2-18x+79=0

a = 1; b = -18; c = +79;
Δ = b2-4ac
Δ = -182-4·1·79
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{2}}{2*1}=\frac{18-2\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{2}}{2*1}=\frac{18+2\sqrt{2}}{2}
$