8n^2=488

Solution for 8n^2=488 equation:

8n^2=488

We move all terms to the left:

8n^2-(488)=0

a = 8; b = 0; c = -488;
Δ = b2-4ac
Δ = 02-4·8·(-488)
Δ = 15616
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:

$\sqrt{\Delta}=\sqrt{15616}=\sqrt{256*61}=\sqrt{256}*\sqrt{61}=16\sqrt{61}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{61}}{2*8}=\frac{0-16\sqrt{61}}{16}
=-\frac{16\sqrt{61}}{16}
=-\sqrt{61}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{61}}{2*8}=\frac{0+16\sqrt{61}}{16}
=\frac{16\sqrt{61}}{16}
=\sqrt{61}
$