-6n^2+2n=-8

Solution for -6n^2+2n=-8 equation:

-6n^2+2n=-8

We move all terms to the left:

-6n^2+2n-(-8)=0

We add all the numbers together, and all the variables

-6n^2+2n+8=0

a = -6; b = 2; c = +8;
Δ = b2-4ac
Δ = 22-4·(-6)·8
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-14}{2*-6}=\frac{-16}{-12}
=1+1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+14}{2*-6}=\frac{12}{-12}
=-1
$