15n(n+2)=4n-8

Solution for 15n(n+2)=4n-8 equation:

15n(n+2)=4n-8

We move all terms to the left:

15n(n+2)-(4n-8)=0

We multiply parentheses

15n^2+30n-(4n-8)=0

We get rid of parentheses

15n^2+30n-4n+8=0

We add all the numbers together, and all the variables

15n^2+26n+8=0

a = 15; b = 26; c = +8;
Δ = b2-4ac
Δ = 262-4·15·8
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-14}{2*15}=\frac{-40}{30}
=-1+1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+14}{2*15}=\frac{-12}{30}
=-2/5
$