15n^2+17n-4=9n^2+9n+10

Solution for 15n^2+17n-4=9n^2+9n+10 equation:

15n^2+17n-4=9n^2+9n+10

We move all terms to the left:

15n^2+17n-4-(9n^2+9n+10)=0

We get rid of parentheses

15n^2-9n^2+17n-9n-10-4=0

We add all the numbers together, and all the variables

6n^2+8n-14=0

a = 6; b = 8; c = -14;
Δ = b2-4ac
Δ = 82-4·6·(-14)
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{-(8)-20}{2*6}=\frac{-28}{12}
=-2+1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+20}{2*6}=\frac{12}{12}
=1
$