x^2=6000

Solution for x^2=6000 equation:

x^2=6000

We move all terms to the left:

x^2-(6000)=0

a = 1; b = 0; c = -6000;
Δ = b2-4ac
Δ = 02-4·1·(-6000)
Δ = 24000
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:

$\sqrt{\Delta}=\sqrt{24000}=\sqrt{1600*15}=\sqrt{1600}*\sqrt{15}=40\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{15}}{2*1}=\frac{0-40\sqrt{15}}{2}
=-\frac{40\sqrt{15}}{2}
=-20\sqrt{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{15}}{2*1}=\frac{0+40\sqrt{15}}{2}
=\frac{40\sqrt{15}}{2}
=20\sqrt{15}
$