(4x+12)2x=180

Solution for (4x+12)2x=180 equation:

(4x+12)2x=180

We move all terms to the left:

(4x+12)2x-(180)=0

We multiply parentheses

8x^2+24x-180=0

a = 8; b = 24; c = -180;
Δ = b2-4ac
Δ = 242-4·8·(-180)
Δ = 6336
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:

$\sqrt{\Delta}=\sqrt{6336}=\sqrt{576*11}=\sqrt{576}*\sqrt{11}=24\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24\sqrt{11}}{2*8}=\frac{-24-24\sqrt{11}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24\sqrt{11}}{2*8}=\frac{-24+24\sqrt{11}}{16}
$