10a^2-500=0

Solution for 10a^2-500=0 equation:

10a^2-500=0

a = 10; b = 0; c = -500;
Δ = b2-4ac
Δ = 02-4·10·(-500)
Δ = 20000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20000}=\sqrt{10000*2}=\sqrt{10000}*\sqrt{2}=100\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100\sqrt{2}}{2*10}=\frac{0-100\sqrt{2}}{20}
=-\frac{100\sqrt{2}}{20}
=-5\sqrt{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100\sqrt{2}}{2*10}=\frac{0+100\sqrt{2}}{20}
=\frac{100\sqrt{2}}{20}
=5\sqrt{2}
$