(x-2)(x+2)+13=8x

Solution for (x-2)(x+2)+13=8x equation:

(x-2)(x+2)+13=8x

We move all terms to the left:

(x-2)(x+2)+13-(8x)=0

We add all the numbers together, and all the variables

-8x+(x-2)(x+2)+13=0

We use the square of the difference formula

x^2-8x-4+13=0

We add all the numbers together, and all the variables

x^2-8x+9=0

a = 1; b = -8; c = +9;
Δ = b2-4ac
Δ = -82-4·1·9
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{7}}{2*1}=\frac{8-2\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{7}}{2*1}=\frac{8+2\sqrt{7}}{2}
$