10000x=2x^2

Solution for 10000x=2x^2 equation:

10000x=2x^2

We move all terms to the left:

10000x-(2x^2)=0

determiningTheFunctionDomain
-2x^2+10000x=0

a = -2; b = 10000; c = 0;
Δ = b2-4ac
Δ = 100002-4·(-2)·0
Δ = 100000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100000000}=10000$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10000)-10000}{2*-2}=\frac{-20000}{-4}
=+5000
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10000)+10000}{2*-2}=\frac{0}{-4}
=0
$