(5n+23)(3n+37)=180

Solution for (5n+23)(3n+37)=180 equation:

(5n+23)(3n+37)=180

We move all terms to the left:

(5n+23)(3n+37)-(180)=0

We multiply parentheses ..

(+15n^2+185n+69n+851)-180=0

We get rid of parentheses

15n^2+185n+69n+851-180=0

We add all the numbers together, and all the variables

15n^2+254n+671=0

a = 15; b = 254; c = +671;
Δ = b2-4ac
Δ = 2542-4·15·671
Δ = 24256
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:

$\sqrt{\Delta}=\sqrt{24256}=\sqrt{64*379}=\sqrt{64}*\sqrt{379}=8\sqrt{379}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(254)-8\sqrt{379}}{2*15}=\frac{-254-8\sqrt{379}}{30}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(254)+8\sqrt{379}}{2*15}=\frac{-254+8\sqrt{379}}{30}
$