6n^2+47n=8

Solution for 6n^2+47n=8 equation:

6n^2+47n=8

We move all terms to the left:

6n^2+47n-(8)=0

a = 6; b = 47; c = -8;
Δ = b2-4ac
Δ = 472-4·6·(-8)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-49}{2*6}=\frac{-96}{12}
=-8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+49}{2*6}=\frac{2}{12}
=1/6
$