8n^2-71-90=0

Solution for 8n^2-71-90=0 equation:

8n^2-71-90=0

We add all the numbers together, and all the variables

8n^2-161=0

a = 8; b = 0; c = -161;
Δ = b2-4ac
Δ = 02-4·8·(-161)
Δ = 5152
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:

$\sqrt{\Delta}=\sqrt{5152}=\sqrt{16*322}=\sqrt{16}*\sqrt{322}=4\sqrt{322}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{322}}{2*8}=\frac{0-4\sqrt{322}}{16}
=-\frac{4\sqrt{322}}{16}
=-\frac{\sqrt{322}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{322}}{2*8}=\frac{0+4\sqrt{322}}{16}
=\frac{4\sqrt{322}}{16}
=\frac{\sqrt{322}}{4}
$