(4n+6)(2n+60)=180

Solution for (4n+6)(2n+60)=180 equation:

(4n+6)(2n+60)=180

We move all terms to the left:

(4n+6)(2n+60)-(180)=0

We multiply parentheses ..

(+8n^2+240n+12n+360)-180=0

We get rid of parentheses

8n^2+240n+12n+360-180=0

We add all the numbers together, and all the variables

8n^2+252n+180=0

a = 8; b = 252; c = +180;
Δ = b2-4ac
Δ = 2522-4·8·180
Δ = 57744
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:

$\sqrt{\Delta}=\sqrt{57744}=\sqrt{144*401}=\sqrt{144}*\sqrt{401}=12\sqrt{401}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(252)-12\sqrt{401}}{2*8}=\frac{-252-12\sqrt{401}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(252)+12\sqrt{401}}{2*8}=\frac{-252+12\sqrt{401}}{16}
$