x=250x-4x^2

Solution for x=250x-4x^2 equation:

x=250x-4x^2

We move all terms to the left:

x-(250x-4x^2)=0

We get rid of parentheses

4x^2-250x+x=0

We add all the numbers together, and all the variables

4x^2-249x=0

a = 4; b = -249; c = 0;
Δ = b2-4ac
Δ = -2492-4·4·0
Δ = 62001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{62001}=249$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-249)-249}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-249)+249}{2*4}=\frac{498}{8}
=62+1/4
$