(3x+2)(9x+6)=180

Solution for (3x+2)(9x+6)=180 equation:

(3x+2)(9x+6)=180

We move all terms to the left:

(3x+2)(9x+6)-(180)=0

We multiply parentheses ..

(+27x^2+18x+18x+12)-180=0

We get rid of parentheses

27x^2+18x+18x+12-180=0

We add all the numbers together, and all the variables

27x^2+36x-168=0

a = 27; b = 36; c = -168;
Δ = b2-4ac
Δ = 362-4·27·(-168)
Δ = 19440
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:

$\sqrt{\Delta}=\sqrt{19440}=\sqrt{1296*15}=\sqrt{1296}*\sqrt{15}=36\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36\sqrt{15}}{2*27}=\frac{-36-36\sqrt{15}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36\sqrt{15}}{2*27}=\frac{-36+36\sqrt{15}}{54}
$