x^2=1000x

Solution for x^2=1000x equation:

x^2=1000x

We move all terms to the left:

x^2-(1000x)=0

a = 1; b = -1000; c = 0;
Δ = b2-4ac
Δ = -10002-4·1·0
Δ = 1000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1000000}=1000$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1000)-1000}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1000)+1000}{2*1}=\frac{2000}{2}
=1000
$