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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+12x^2-27x+28x-63)-180=0

We get rid of parentheses

12x^2-27x+28x-63-180=0

We add all the numbers together, and all the variables

12x^2+x-243=0

a = 12; b = 1; c = -243;
Δ = b2-4ac
Δ = 12-4·12·(-243)
Δ = 11665
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{11665}}{2*12}=\frac{-1-\sqrt{11665}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{11665}}{2*12}=\frac{-1+\sqrt{11665}}{24}
$