6n^2=104-2n

Solution for 6n^2=104-2n equation:

6n^2=104-2n

We move all terms to the left:

6n^2-(104-2n)=0

We add all the numbers together, and all the variables

6n^2-(-2n+104)=0

We get rid of parentheses

6n^2+2n-104=0

a = 6; b = 2; c = -104;
Δ = b2-4ac
Δ = 22-4·6·(-104)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-50}{2*6}=\frac{-52}{12}
=-4+1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+50}{2*6}=\frac{48}{12}
=4
$