15X(n+8)=5

Solution for 15X(n+8)=5 equation:

15X(X+8)=5

We move all terms to the left:

15X(X+8)-(5)=0

We multiply parentheses

15X^2+120X-5=0

a = 15; b = 120; c = -5;
Δ = b2-4ac
Δ = 1202-4·15·(-5)
Δ = 14700
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14700}=\sqrt{4900*3}=\sqrt{4900}*\sqrt{3}=70\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-70\sqrt{3}}{2*15}=\frac{-120-70\sqrt{3}}{30}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+70\sqrt{3}}{2*15}=\frac{-120+70\sqrt{3}}{30}
$