43(x+15)3x=180

Solution for 43(x+15)3x=180 equation:

43(x+15)3x=180

We move all terms to the left:

43(x+15)3x-(180)=0

We multiply parentheses

129x^2+1935x-180=0

a = 129; b = 1935; c = -180;
Δ = b2-4ac
Δ = 19352-4·129·(-180)
Δ = 3837105
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:

$\sqrt{\Delta}=\sqrt{3837105}=\sqrt{9*426345}=\sqrt{9}*\sqrt{426345}=3\sqrt{426345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1935)-3\sqrt{426345}}{2*129}=\frac{-1935-3\sqrt{426345}}{258}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1935)+3\sqrt{426345}}{2*129}=\frac{-1935+3\sqrt{426345}}{258}
$