(2n+15)(5n+11)=180

Solution for (2n+15)(5n+11)=180 equation:

(2n+15)(5n+11)=180

We move all terms to the left:

(2n+15)(5n+11)-(180)=0

We multiply parentheses ..

(+10n^2+22n+75n+165)-180=0

We get rid of parentheses

10n^2+22n+75n+165-180=0

We add all the numbers together, and all the variables

10n^2+97n-15=0

a = 10; b = 97; c = -15;
Δ = b2-4ac
Δ = 972-4·10·(-15)
Δ = 10009
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(97)-\sqrt{10009}}{2*10}=\frac{-97-\sqrt{10009}}{20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(97)+\sqrt{10009}}{2*10}=\frac{-97+\sqrt{10009}}{20}
$