x*x=3000

Solution for x*x=3000 equation:

x*x=3000

We move all terms to the left:

x*x-(3000)=0

Wy multiply elements

x^2-3000=0

a = 1; b = 0; c = -3000;
Δ = b2-4ac
Δ = 02-4·1·(-3000)
Δ = 12000
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:

$\sqrt{\Delta}=\sqrt{12000}=\sqrt{400*30}=\sqrt{400}*\sqrt{30}=20\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{30}}{2*1}=\frac{0-20\sqrt{30}}{2}
=-\frac{20\sqrt{30}}{2}
=-10\sqrt{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{30}}{2*1}=\frac{0+20\sqrt{30}}{2}
=\frac{20\sqrt{30}}{2}
=10\sqrt{30}
$