8a^2-1000=0

Solution for 8a^2-1000=0 equation:

8a^2-1000=0

a = 8; b = 0; c = -1000;
Δ = b2-4ac
Δ = 02-4·8·(-1000)
Δ = 32000
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:

$\sqrt{\Delta}=\sqrt{32000}=\sqrt{6400*5}=\sqrt{6400}*\sqrt{5}=80\sqrt{5}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{5}}{2*8}=\frac{0-80\sqrt{5}}{16}
=-\frac{80\sqrt{5}}{16}
=-5\sqrt{5}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{5}}{2*8}=\frac{0+80\sqrt{5}}{16}
=\frac{80\sqrt{5}}{16}
=5\sqrt{5}
$