x*x=600000

Solution for x*x=600000 equation:

x*x=600000

We move all terms to the left:

x*x-(600000)=0

Wy multiply elements

x^2-600000=0

a = 1; b = 0; c = -600000;
Δ = b2-4ac
Δ = 02-4·1·(-600000)
Δ = 2400000
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:

$\sqrt{\Delta}=\sqrt{2400000}=\sqrt{160000*15}=\sqrt{160000}*\sqrt{15}=400\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-400\sqrt{15}}{2*1}=\frac{0-400\sqrt{15}}{2}
=-\frac{400\sqrt{15}}{2}
=-200\sqrt{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+400\sqrt{15}}{2*1}=\frac{0+400\sqrt{15}}{2}
=\frac{400\sqrt{15}}{2}
=200\sqrt{15}
$