6n^2+46n=8

Solution for 6n^2+46n=8 equation:

6n^2+46n=8

We move all terms to the left:

6n^2+46n-(8)=0

a = 6; b = 46; c = -8;
Δ = b2-4ac
Δ = 462-4·6·(-8)
Δ = 2308
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:

$\sqrt{\Delta}=\sqrt{2308}=\sqrt{4*577}=\sqrt{4}*\sqrt{577}=2\sqrt{577}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{577}}{2*6}=\frac{-46-2\sqrt{577}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{577}}{2*6}=\frac{-46+2\sqrt{577}}{12}
$