8n^2+5=797

Solution for 8n^2+5=797 equation:

8n^2+5=797

We move all terms to the left:

8n^2+5-(797)=0

We add all the numbers together, and all the variables

8n^2-792=0

a = 8; b = 0; c = -792;
Δ = b2-4ac
Δ = 02-4·8·(-792)
Δ = 25344
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:

$\sqrt{\Delta}=\sqrt{25344}=\sqrt{2304*11}=\sqrt{2304}*\sqrt{11}=48\sqrt{11}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{11}}{2*8}=\frac{0-48\sqrt{11}}{16}
=-\frac{48\sqrt{11}}{16}
=-3\sqrt{11}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{11}}{2*8}=\frac{0+48\sqrt{11}}{16}
=\frac{48\sqrt{11}}{16}
=3\sqrt{11}
$