10n^2=2n+8

Solution for 10n^2=2n+8 equation:

10n^2=2n+8

We move all terms to the left:

10n^2-(2n+8)=0

We get rid of parentheses

10n^2-2n-8=0

a = 10; b = -2; c = -8;
Δ = b2-4ac
Δ = -22-4·10·(-8)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-18}{2*10}=\frac{-16}{20}
=-4/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+18}{2*10}=\frac{20}{20}
=1
$