(6x+12)(4x+18)=180

Solution for (6x+12)(4x+18)=180 equation:

(6x+12)(4x+18)=180

We move all terms to the left:

(6x+12)(4x+18)-(180)=0

We multiply parentheses ..

(+24x^2+108x+48x+216)-180=0

We get rid of parentheses

24x^2+108x+48x+216-180=0

We add all the numbers together, and all the variables

24x^2+156x+36=0

a = 24; b = 156; c = +36;
Δ = b2-4ac
Δ = 1562-4·24·36
Δ = 20880
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:

$\sqrt{\Delta}=\sqrt{20880}=\sqrt{144*145}=\sqrt{144}*\sqrt{145}=12\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(156)-12\sqrt{145}}{2*24}=\frac{-156-12\sqrt{145}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(156)+12\sqrt{145}}{2*24}=\frac{-156+12\sqrt{145}}{48}
$