6n^2+4=93

Solution for 6n^2+4=93 equation:

6n^2+4=93

We move all terms to the left:

6n^2+4-(93)=0

We add all the numbers together, and all the variables

6n^2-89=0

a = 6; b = 0; c = -89;
Δ = b2-4ac
Δ = 02-4·6·(-89)
Δ = 2136
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:

$\sqrt{\Delta}=\sqrt{2136}=\sqrt{4*534}=\sqrt{4}*\sqrt{534}=2\sqrt{534}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{534}}{2*6}=\frac{0-2\sqrt{534}}{12}
=-\frac{2\sqrt{534}}{12}
=-\frac{\sqrt{534}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{534}}{2*6}=\frac{0+2\sqrt{534}}{12}
=\frac{2\sqrt{534}}{12}
=\frac{\sqrt{534}}{6}
$