6n^2+4=502

Solution for 6n^2+4=502 equation:

6n^2+4=502

We move all terms to the left:

6n^2+4-(502)=0

We add all the numbers together, and all the variables

6n^2-498=0

a = 6; b = 0; c = -498;
Δ = b2-4ac
Δ = 02-4·6·(-498)
Δ = 11952
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:

$\sqrt{\Delta}=\sqrt{11952}=\sqrt{144*83}=\sqrt{144}*\sqrt{83}=12\sqrt{83}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{83}}{2*6}=\frac{0-12\sqrt{83}}{12}
=-\frac{12\sqrt{83}}{12}
=-\sqrt{83}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{83}}{2*6}=\frac{0+12\sqrt{83}}{12}
=\frac{12\sqrt{83}}{12}
=\sqrt{83}
$