x^2=12000

Solution for x^2=12000 equation:

x^2=12000

We move all terms to the left:

x^2-(12000)=0

a = 1; b = 0; c = -12000;
Δ = b2-4ac
Δ = 02-4·1·(-12000)
Δ = 48000
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:

$\sqrt{\Delta}=\sqrt{48000}=\sqrt{1600*30}=\sqrt{1600}*\sqrt{30}=40\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{30}}{2*1}=\frac{0-40\sqrt{30}}{2}
=-\frac{40\sqrt{30}}{2}
=-20\sqrt{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{30}}{2*1}=\frac{0+40\sqrt{30}}{2}
=\frac{40\sqrt{30}}{2}
=20\sqrt{30}
$