6n^2+4n=112

Solution for 6n^2+4n=112 equation:

6n^2+4n=112

We move all terms to the left:

6n^2+4n-(112)=0

a = 6; b = 4; c = -112;
Δ = b2-4ac
Δ = 42-4·6·(-112)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-52}{2*6}=\frac{-56}{12}
=-4+2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+52}{2*6}=\frac{48}{12}
=4
$