114=(4n+6)(2n)

Solution for 114=(4n+6)(2n) equation:

114=(4n+6)(2n)

We move all terms to the left:

114-((4n+6)(2n))=0


We calculate terms in parentheses: -((4n+6)2n), so:

(4n+6)2n

We multiply parentheses

8n^2+12n

Back to the equation:

-(8n^2+12n)


We get rid of parentheses

-8n^2-12n+114=0

a = -8; b = -12; c = +114;
Δ = b2-4ac
Δ = -122-4·(-8)·114
Δ = 3792
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:

$\sqrt{\Delta}=\sqrt{3792}=\sqrt{16*237}=\sqrt{16}*\sqrt{237}=4\sqrt{237}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{237}}{2*-8}=\frac{12-4\sqrt{237}}{-16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{237}}{2*-8}=\frac{12+4\sqrt{237}}{-16}
$