(3n-18)(2n-27)=180

Solution for (3n-18)(2n-27)=180 equation:

(3n-18)(2n-27)=180

We move all terms to the left:

(3n-18)(2n-27)-(180)=0

We multiply parentheses ..

(+6n^2-81n-36n+486)-180=0

We get rid of parentheses

6n^2-81n-36n+486-180=0

We add all the numbers together, and all the variables

6n^2-117n+306=0

a = 6; b = -117; c = +306;
Δ = b2-4ac
Δ = -1172-4·6·306
Δ = 6345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6345}=\sqrt{9*705}=\sqrt{9}*\sqrt{705}=3\sqrt{705}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-117)-3\sqrt{705}}{2*6}=\frac{117-3\sqrt{705}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-117)+3\sqrt{705}}{2*6}=\frac{117+3\sqrt{705}}{12}
$