8n^2=25

Solution for 8n^2=25 equation:

8n^2=25

We move all terms to the left:

8n^2-(25)=0

a = 8; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·8·(-25)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{2}}{2*8}=\frac{0-20\sqrt{2}}{16}
=-\frac{20\sqrt{2}}{16}
=-\frac{5\sqrt{2}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{2}}{2*8}=\frac{0+20\sqrt{2}}{16}
=\frac{20\sqrt{2}}{16}
=\frac{5\sqrt{2}}{4}
$