2n^2-8n-112=6n

Solution for 2n^2-8n-112=6n equation:

2n^2-8n-112=6n

We move all terms to the left:

2n^2-8n-112-(6n)=0

We add all the numbers together, and all the variables

2n^2-14n-112=0

a = 2; b = -14; c = -112;
Δ = b2-4ac
Δ = -142-4·2·(-112)
Δ = 1092
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1092}=\sqrt{4*273}=\sqrt{4}*\sqrt{273}=2\sqrt{273}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{273}}{2*2}=\frac{14-2\sqrt{273}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{273}}{2*2}=\frac{14+2\sqrt{273}}{4}
$