15n2-15=10n+10n2

Solution for 15n2-15=10n+10n2 equation:

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

We move all terms to the left:

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

We get rid of parentheses

15n^2-10n^2-10n-15=0

We add all the numbers together, and all the variables

5n^2-10n-15=0

a = 5; b = -10; c = -15;
Δ = b2-4ac
Δ = -102-4·5·(-15)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-20}{2*5}=\frac{-10}{10}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+20}{2*5}=\frac{30}{10}
=3
$