(4x-7)(3x+9)=180

Solution for (4x-7)(3x+9)=180 equation:

(4x-7)(3x+9)=180

We move all terms to the left:

(4x-7)(3x+9)-(180)=0

We multiply parentheses ..

(+12x^2+36x-21x-63)-180=0

We get rid of parentheses

12x^2+36x-21x-63-180=0

We add all the numbers together, and all the variables

12x^2+15x-243=0

a = 12; b = 15; c = -243;
Δ = b2-4ac
Δ = 152-4·12·(-243)
Δ = 11889
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:

$\sqrt{\Delta}=\sqrt{11889}=\sqrt{9*1321}=\sqrt{9}*\sqrt{1321}=3\sqrt{1321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{1321}}{2*12}=\frac{-15-3\sqrt{1321}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{1321}}{2*12}=\frac{-15+3\sqrt{1321}}{24}
$