(X-57)2x=180

Solution for (X-57)2x=180 equation:

(X-57)2X=180

We move all terms to the left:

(X-57)2X-(180)=0

We multiply parentheses

2X^2-114X-180=0

a = 2; b = -114; c = -180;
Δ = b2-4ac
Δ = -1142-4·2·(-180)
Δ = 14436
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:

$\sqrt{\Delta}=\sqrt{14436}=\sqrt{36*401}=\sqrt{36}*\sqrt{401}=6\sqrt{401}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-6\sqrt{401}}{2*2}=\frac{114-6\sqrt{401}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+6\sqrt{401}}{2*2}=\frac{114+6\sqrt{401}}{4}
$