(6x-3)(2x+13)=180

Solution for (6x-3)(2x+13)=180 equation:

(6x-3)(2x+13)=180

We move all terms to the left:

(6x-3)(2x+13)-(180)=0

We multiply parentheses ..

(+12x^2+78x-6x-39)-180=0

We get rid of parentheses

12x^2+78x-6x-39-180=0

We add all the numbers together, and all the variables

12x^2+72x-219=0

a = 12; b = 72; c = -219;
Δ = b2-4ac
Δ = 722-4·12·(-219)
Δ = 15696
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:

$\sqrt{\Delta}=\sqrt{15696}=\sqrt{144*109}=\sqrt{144}*\sqrt{109}=12\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-12\sqrt{109}}{2*12}=\frac{-72-12\sqrt{109}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+12\sqrt{109}}{2*12}=\frac{-72+12\sqrt{109}}{24}
$