15n^2+34n+10=-5

Solution for 15n^2+34n+10=-5 equation:

15n^2+34n+10=-5

We move all terms to the left:

15n^2+34n+10-(-5)=0

We add all the numbers together, and all the variables

15n^2+34n+15=0

a = 15; b = 34; c = +15;
Δ = b2-4ac
Δ = 342-4·15·15
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-16}{2*15}=\frac{-50}{30}
=-1+2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+16}{2*15}=\frac{-18}{30}
=-3/5
$