(3x)(2x-13)+63=180

Solution for (3x)(2x-13)+63=180 equation:

(3x)(2x-13)+63=180

We move all terms to the left:

(3x)(2x-13)+63-(180)=0

We add all the numbers together, and all the variables

3x(2x-13)-117=0

We multiply parentheses

6x^2-39x-117=0

a = 6; b = -39; c = -117;
Δ = b2-4ac
Δ = -392-4·6·(-117)
Δ = 4329
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:

$\sqrt{\Delta}=\sqrt{4329}=\sqrt{9*481}=\sqrt{9}*\sqrt{481}=3\sqrt{481}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-3\sqrt{481}}{2*6}=\frac{39-3\sqrt{481}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+3\sqrt{481}}{2*6}=\frac{39+3\sqrt{481}}{12}
$