24000-8x^2=0

Solution for 24000-8x^2=0 equation:

24000-8x^2=0

a = -8; b = 0; c = +24000;
Δ = b2-4ac
Δ = 02-4·(-8)·24000
Δ = 768000
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:

$\sqrt{\Delta}=\sqrt{768000}=\sqrt{25600*30}=\sqrt{25600}*\sqrt{30}=160\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-160\sqrt{30}}{2*-8}=\frac{0-160\sqrt{30}}{-16}
=-\frac{160\sqrt{30}}{-16}
=-\frac{10\sqrt{30}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+160\sqrt{30}}{2*-8}=\frac{0+160\sqrt{30}}{-16}
=\frac{160\sqrt{30}}{-16}
=\frac{10\sqrt{30}}{-1}
$