7n^2=488

Solution for 7n^2=488 equation:

7n^2=488

We move all terms to the left:

7n^2-(488)=0

a = 7; b = 0; c = -488;
Δ = b2-4ac
Δ = 02-4·7·(-488)
Δ = 13664
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:

$\sqrt{\Delta}=\sqrt{13664}=\sqrt{16*854}=\sqrt{16}*\sqrt{854}=4\sqrt{854}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{854}}{2*7}=\frac{0-4\sqrt{854}}{14}
=-\frac{4\sqrt{854}}{14}
=-\frac{2\sqrt{854}}{7}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{854}}{2*7}=\frac{0+4\sqrt{854}}{14}
=\frac{4\sqrt{854}}{14}
=\frac{2\sqrt{854}}{7}
$