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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+54x^2+81x+36x+54)-180=0

We get rid of parentheses

54x^2+81x+36x+54-180=0

We add all the numbers together, and all the variables

54x^2+117x-126=0

a = 54; b = 117; c = -126;
Δ = b2-4ac
Δ = 1172-4·54·(-126)
Δ = 40905
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:

$\sqrt{\Delta}=\sqrt{40905}=\sqrt{81*505}=\sqrt{81}*\sqrt{505}=9\sqrt{505}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(117)-9\sqrt{505}}{2*54}=\frac{-117-9\sqrt{505}}{108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(117)+9\sqrt{505}}{2*54}=\frac{-117+9\sqrt{505}}{108}
$