(12x+3)(7x-13)=180

Solution for (12x+3)(7x-13)=180 equation:

(12x+3)(7x-13)=180

We move all terms to the left:

(12x+3)(7x-13)-(180)=0

We multiply parentheses ..

(+84x^2-156x+21x-39)-180=0

We get rid of parentheses

84x^2-156x+21x-39-180=0

We add all the numbers together, and all the variables

84x^2-135x-219=0

a = 84; b = -135; c = -219;
Δ = b2-4ac
Δ = -1352-4·84·(-219)
Δ = 91809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{91809}=303$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-135)-303}{2*84}=\frac{-168}{168}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+303}{2*84}=\frac{438}{168}
=2+17/28
$