6n2+5=371

Solution for 6n2+5=371 equation:

6n^2+5=371

We move all terms to the left:

6n^2+5-(371)=0

We add all the numbers together, and all the variables

6n^2-366=0

a = 6; b = 0; c = -366;
Δ = b2-4ac
Δ = 02-4·6·(-366)
Δ = 8784
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:

$\sqrt{\Delta}=\sqrt{8784}=\sqrt{144*61}=\sqrt{144}*\sqrt{61}=12\sqrt{61}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{61}}{2*6}=\frac{0-12\sqrt{61}}{12}
=-\frac{12\sqrt{61}}{12}
=-\sqrt{61}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{61}}{2*6}=\frac{0+12\sqrt{61}}{12}
=\frac{12\sqrt{61}}{12}
=\sqrt{61}
$