200x=x^2/4

Solution for 200x=x^2/4 equation:

200x=x^2/4

We move all terms to the left:

200x-(x^2/4)=0

We get rid of parentheses

-x^2/4+200x=0

We multiply all the terms by the denominator


-x^2+200x*4=0

We add all the numbers together, and all the variables

-1x^2+200x*4=0

Wy multiply elements

-1x^2+800x=0

a = -1; b = 800; c = 0;
Δ = b2-4ac
Δ = 8002-4·(-1)·0
Δ = 640000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{640000}=800$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(800)-800}{2*-1}=\frac{-1600}{-2}
=+800
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(800)+800}{2*-1}=\frac{0}{-2}
=0
$