(3x-12)(2x-23)=180

Solution for (3x-12)(2x-23)=180 equation:

(3x-12)(2x-23)=180

We move all terms to the left:

(3x-12)(2x-23)-(180)=0

We multiply parentheses ..

(+6x^2-69x-24x+276)-180=0

We get rid of parentheses

6x^2-69x-24x+276-180=0

We add all the numbers together, and all the variables

6x^2-93x+96=0

a = 6; b = -93; c = +96;
Δ = b2-4ac
Δ = -932-4·6·96
Δ = 6345
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:

$\sqrt{\Delta}=\sqrt{6345}=\sqrt{9*705}=\sqrt{9}*\sqrt{705}=3\sqrt{705}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-93)-3\sqrt{705}}{2*6}=\frac{93-3\sqrt{705}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-93)+3\sqrt{705}}{2*6}=\frac{93+3\sqrt{705}}{12}
$