x^2-8x-64=165

Solution for x^2-8x-64=165 equation:

x^2-8x-64=165

We move all terms to the left:

x^2-8x-64-(165)=0

We add all the numbers together, and all the variables

x^2-8x-229=0

a = 1; b = -8; c = -229;
Δ = b2-4ac
Δ = -82-4·1·(-229)
Δ = 980
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:

$\sqrt{\Delta}=\sqrt{980}=\sqrt{196*5}=\sqrt{196}*\sqrt{5}=14\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-14\sqrt{5}}{2*1}=\frac{8-14\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+14\sqrt{5}}{2*1}=\frac{8+14\sqrt{5}}{2}
$