8x^2=500

Solution for 8x^2=500 equation:

8x^2=500

We move all terms to the left:

8x^2-(500)=0

a = 8; b = 0; c = -500;
Δ = b2-4ac
Δ = 02-4·8·(-500)
Δ = 16000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{16000}=\sqrt{1600*10}=\sqrt{1600}*\sqrt{10}=40\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{10}}{2*8}=\frac{0-40\sqrt{10}}{16}
=-\frac{40\sqrt{10}}{16}
=-\frac{5\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{10}}{2*8}=\frac{0+40\sqrt{10}}{16}
=\frac{40\sqrt{10}}{16}
=\frac{5\sqrt{10}}{2}
$