7n2-2=313

Solution for 7n2-2=313 equation:

7n^2-2=313

We move all terms to the left:

7n^2-2-(313)=0

We add all the numbers together, and all the variables

7n^2-315=0

a = 7; b = 0; c = -315;
Δ = b2-4ac
Δ = 02-4·7·(-315)
Δ = 8820
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:

$\sqrt{\Delta}=\sqrt{8820}=\sqrt{1764*5}=\sqrt{1764}*\sqrt{5}=42\sqrt{5}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-42\sqrt{5}}{2*7}=\frac{0-42\sqrt{5}}{14}
=-\frac{42\sqrt{5}}{14}
=-3\sqrt{5}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+42\sqrt{5}}{2*7}=\frac{0+42\sqrt{5}}{14}
=\frac{42\sqrt{5}}{14}
=3\sqrt{5}
$