(x+8)4x=180

Solution for (x+8)4x=180 equation:

(x+8)4x=180

We move all terms to the left:

(x+8)4x-(180)=0

We multiply parentheses

4x^2+32x-180=0

a = 4; b = 32; c = -180;
Δ = b2-4ac
Δ = 322-4·4·(-180)
Δ = 3904
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:

$\sqrt{\Delta}=\sqrt{3904}=\sqrt{64*61}=\sqrt{64}*\sqrt{61}=8\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-8\sqrt{61}}{2*4}=\frac{-32-8\sqrt{61}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+8\sqrt{61}}{2*4}=\frac{-32+8\sqrt{61}}{8}
$