2n(3n+7)=8

Solution for 2n(3n+7)=8 equation:

2n(3n+7)=8

We move all terms to the left:

2n(3n+7)-(8)=0

We multiply parentheses

6n^2+14n-8=0

a = 6; b = 14; c = -8;
Δ = b2-4ac
Δ = 142-4·6·(-8)
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{97}}{2*6}=\frac{-14-2\sqrt{97}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{97}}{2*6}=\frac{-14+2\sqrt{97}}{12}
$