(3x+22)(4x-6)=180

Solution for (3x+22)(4x-6)=180 equation:

(3x+22)(4x-6)=180

We move all terms to the left:

(3x+22)(4x-6)-(180)=0

We multiply parentheses ..

(+12x^2-18x+88x-132)-180=0

We get rid of parentheses

12x^2-18x+88x-132-180=0

We add all the numbers together, and all the variables

12x^2+70x-312=0

a = 12; b = 70; c = -312;
Δ = b2-4ac
Δ = 702-4·12·(-312)
Δ = 19876
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:

$\sqrt{\Delta}=\sqrt{19876}=\sqrt{4*4969}=\sqrt{4}*\sqrt{4969}=2\sqrt{4969}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-2\sqrt{4969}}{2*12}=\frac{-70-2\sqrt{4969}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+2\sqrt{4969}}{2*12}=\frac{-70+2\sqrt{4969}}{24}
$