(3x+5)2x=360

Solution for (3x+5)2x=360 equation:

(3x+5)2x=360

We move all terms to the left:

(3x+5)2x-(360)=0

We multiply parentheses

6x^2+10x-360=0

a = 6; b = 10; c = -360;
Δ = b2-4ac
Δ = 102-4·6·(-360)
Δ = 8740
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:

$\sqrt{\Delta}=\sqrt{8740}=\sqrt{4*2185}=\sqrt{4}*\sqrt{2185}=2\sqrt{2185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{2185}}{2*6}=\frac{-10-2\sqrt{2185}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{2185}}{2*6}=\frac{-10+2\sqrt{2185}}{12}
$