(12x-7)(4x+9)=180

Solution for (12x-7)(4x+9)=180 equation:

(12x-7)(4x+9)=180

We move all terms to the left:

(12x-7)(4x+9)-(180)=0

We multiply parentheses ..

(+48x^2+108x-28x-63)-180=0

We get rid of parentheses

48x^2+108x-28x-63-180=0

We add all the numbers together, and all the variables

48x^2+80x-243=0

a = 48; b = 80; c = -243;
Δ = b2-4ac
Δ = 802-4·48·(-243)
Δ = 53056
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:

$\sqrt{\Delta}=\sqrt{53056}=\sqrt{64*829}=\sqrt{64}*\sqrt{829}=8\sqrt{829}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-8\sqrt{829}}{2*48}=\frac{-80-8\sqrt{829}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+8\sqrt{829}}{2*48}=\frac{-80+8\sqrt{829}}{96}
$