2n^2-2=8+5n

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

2n^2-2=8+5n

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2n^2-5n-10=0

a = 2; b = -5; c = -10;
Δ = b2-4ac
Δ = -52-4·2·(-10)
Δ = 105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{105}}{2*2}=\frac{5-\sqrt{105}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{105}}{2*2}=\frac{5+\sqrt{105}}{4}
$