6n^2=80-14n

Solution for 6n^2=80-14n equation:

6n^2=80-14n

We move all terms to the left:

6n^2-(80-14n)=0

We add all the numbers together, and all the variables

6n^2-(-14n+80)=0

We get rid of parentheses

6n^2+14n-80=0

a = 6; b = 14; c = -80;
Δ = b2-4ac
Δ = 142-4·6·(-80)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-46}{2*6}=\frac{-60}{12}
=-5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+46}{2*6}=\frac{32}{12}
=2+2/3
$