(3x-4)(4x+24)=180

Solution for (3x-4)(4x+24)=180 equation:

(3x-4)(4x+24)=180

We move all terms to the left:

(3x-4)(4x+24)-(180)=0

We multiply parentheses ..

(+12x^2+72x-16x-96)-180=0

We get rid of parentheses

12x^2+72x-16x-96-180=0

We add all the numbers together, and all the variables

12x^2+56x-276=0

a = 12; b = 56; c = -276;
Δ = b2-4ac
Δ = 562-4·12·(-276)
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-128}{2*12}=\frac{-184}{24}
=-7+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+128}{2*12}=\frac{72}{24}
=3
$