2(3x+5)2x=180

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

2(3x+5)2x=180

We move all terms to the left:

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

We multiply parentheses

12x^2+20x-180=0

a = 12; b = 20; c = -180;
Δ = b2-4ac
Δ = 202-4·12·(-180)
Δ = 9040
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:

$\sqrt{\Delta}=\sqrt{9040}=\sqrt{16*565}=\sqrt{16}*\sqrt{565}=4\sqrt{565}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{565}}{2*12}=\frac{-20-4\sqrt{565}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{565}}{2*12}=\frac{-20+4\sqrt{565}}{24}
$