15n^2+50n+32=-2n

Solution for 15n^2+50n+32=-2n equation:

15n^2+50n+32=-2n

We move all terms to the left:

15n^2+50n+32-(-2n)=0

We get rid of parentheses

15n^2+50n+2n+32=0

We add all the numbers together, and all the variables

15n^2+52n+32=0

a = 15; b = 52; c = +32;
Δ = b2-4ac
Δ = 522-4·15·32
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-28}{2*15}=\frac{-80}{30}
=-2+2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+28}{2*15}=\frac{-24}{30}
=-4/5
$