(3x-5)2x=180

Solution for (3x-5)2x=180 equation:

(3x-5)2x=180

We move all terms to the left:

(3x-5)2x-(180)=0

We multiply parentheses

6x^2-10x-180=0

a = 6; b = -10; c = -180;
Δ = b2-4ac
Δ = -102-4·6·(-180)
Δ = 4420
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:

$\sqrt{\Delta}=\sqrt{4420}=\sqrt{4*1105}=\sqrt{4}*\sqrt{1105}=2\sqrt{1105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{1105}}{2*6}=\frac{10-2\sqrt{1105}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{1105}}{2*6}=\frac{10+2\sqrt{1105}}{12}
$