(6x-2)(4x+3)=180

Solution for (6x-2)(4x+3)=180 equation:

(6x-2)(4x+3)=180

We move all terms to the left:

(6x-2)(4x+3)-(180)=0

We multiply parentheses ..

(+24x^2+18x-8x-6)-180=0

We get rid of parentheses

24x^2+18x-8x-6-180=0

We add all the numbers together, and all the variables

24x^2+10x-186=0

a = 24; b = 10; c = -186;
Δ = b2-4ac
Δ = 102-4·24·(-186)
Δ = 17956
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17956}=134$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-134}{2*24}=\frac{-144}{48}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+134}{2*24}=\frac{124}{48}
=2+7/12
$