(3x+6)(4x-7)=180

Solution for (3x+6)(4x-7)=180 equation:

(3x+6)(4x-7)=180

We move all terms to the left:

(3x+6)(4x-7)-(180)=0

We multiply parentheses ..

(+12x^2-21x+24x-42)-180=0

We get rid of parentheses

12x^2-21x+24x-42-180=0

We add all the numbers together, and all the variables

12x^2+3x-222=0

a = 12; b = 3; c = -222;
Δ = b2-4ac
Δ = 32-4·12·(-222)
Δ = 10665
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:

$\sqrt{\Delta}=\sqrt{10665}=\sqrt{9*1185}=\sqrt{9}*\sqrt{1185}=3\sqrt{1185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{1185}}{2*12}=\frac{-3-3\sqrt{1185}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{1185}}{2*12}=\frac{-3+3\sqrt{1185}}{24}
$