(6x-4)(4x+38)=180

Solution for (6x-4)(4x+38)=180 equation:

(6x-4)(4x+38)=180

We move all terms to the left:

(6x-4)(4x+38)-(180)=0

We multiply parentheses ..

(+24x^2+228x-16x-152)-180=0

We get rid of parentheses

24x^2+228x-16x-152-180=0

We add all the numbers together, and all the variables

24x^2+212x-332=0

a = 24; b = 212; c = -332;
Δ = b2-4ac
Δ = 2122-4·24·(-332)
Δ = 76816
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:

$\sqrt{\Delta}=\sqrt{76816}=\sqrt{16*4801}=\sqrt{16}*\sqrt{4801}=4\sqrt{4801}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(212)-4\sqrt{4801}}{2*24}=\frac{-212-4\sqrt{4801}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(212)+4\sqrt{4801}}{2*24}=\frac{-212+4\sqrt{4801}}{48}
$