(3n+25)(4n+36)=180

Solution for (3n+25)(4n+36)=180 equation:

(3n+25)(4n+36)=180

We move all terms to the left:

(3n+25)(4n+36)-(180)=0

We multiply parentheses ..

(+12n^2+108n+100n+900)-180=0

We get rid of parentheses

12n^2+108n+100n+900-180=0

We add all the numbers together, and all the variables

12n^2+208n+720=0

a = 12; b = 208; c = +720;
Δ = b2-4ac
Δ = 2082-4·12·720
Δ = 8704
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:

$\sqrt{\Delta}=\sqrt{8704}=\sqrt{256*34}=\sqrt{256}*\sqrt{34}=16\sqrt{34}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(208)-16\sqrt{34}}{2*12}=\frac{-208-16\sqrt{34}}{24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(208)+16\sqrt{34}}{2*12}=\frac{-208+16\sqrt{34}}{24}
$