5n^2+8n-2=-7+2n^2

Solution for 5n^2+8n-2=-7+2n^2 equation:

5n^2+8n-2=-7+2n^2

We move all terms to the left:

5n^2+8n-2-(-7+2n^2)=0

We get rid of parentheses

5n^2-2n^2+8n+7-2=0

We add all the numbers together, and all the variables

3n^2+8n+5=0

a = 3; b = 8; c = +5;
Δ = b2-4ac
Δ = 82-4·3·5
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2}{2*3}=\frac{-10}{6}
=-1+2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2}{2*3}=\frac{-6}{6}
=-1
$