8n^2-4=536

Solution for 8n^2-4=536 equation:

8n^2-4=536

We move all terms to the left:

8n^2-4-(536)=0

We add all the numbers together, and all the variables

8n^2-540=0

a = 8; b = 0; c = -540;
Δ = b2-4ac
Δ = 02-4·8·(-540)
Δ = 17280
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:

$\sqrt{\Delta}=\sqrt{17280}=\sqrt{576*30}=\sqrt{576}*\sqrt{30}=24\sqrt{30}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{30}}{2*8}=\frac{0-24\sqrt{30}}{16}
=-\frac{24\sqrt{30}}{16}
=-\frac{3\sqrt{30}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{30}}{2*8}=\frac{0+24\sqrt{30}}{16}
=\frac{24\sqrt{30}}{16}
=\frac{3\sqrt{30}}{2}
$