8n^2+5=237

Solution for 8n^2+5=237 equation:

8n^2+5=237

We move all terms to the left:

8n^2+5-(237)=0

We add all the numbers together, and all the variables

8n^2-232=0

a = 8; b = 0; c = -232;
Δ = b2-4ac
Δ = 02-4·8·(-232)
Δ = 7424
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:

$\sqrt{\Delta}=\sqrt{7424}=\sqrt{256*29}=\sqrt{256}*\sqrt{29}=16\sqrt{29}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{29}}{2*8}=\frac{0-16\sqrt{29}}{16}
=-\frac{16\sqrt{29}}{16}
=-\sqrt{29}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{29}}{2*8}=\frac{0+16\sqrt{29}}{16}
=\frac{16\sqrt{29}}{16}
=\sqrt{29}
$