12n^2=80+28n

Solution for 12n^2=80+28n equation:

12n^2=80+28n

We move all terms to the left:

12n^2-(80+28n)=0

We add all the numbers together, and all the variables

12n^2-(28n+80)=0

We get rid of parentheses

12n^2-28n-80=0

a = 12; b = -28; c = -80;
Δ = b2-4ac
Δ = -282-4·12·(-80)
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-68}{2*12}=\frac{-40}{24}
=-1+2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+68}{2*12}=\frac{96}{24}
=4
$