25/200*x=35+x

Solution for 25/200*x=35+x equation:

25/200x=35+x

We move all terms to the left:

25/200x-(35+x)=0


Domain of the equation: 200x!=0

x!=0/200

x!=0

x∈R


We add all the numbers together, and all the variables

25/200x-(x+35)=0

We get rid of parentheses

25/200x-x-35=0

We multiply all the terms by the denominator


-x*200x-35*200x+25=0

Wy multiply elements

-200x^2-7000x+25=0

a = -200; b = -7000; c = +25;
Δ = b2-4ac
Δ = -70002-4·(-200)·25
Δ = 49020000
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:

$\sqrt{\Delta}=\sqrt{49020000}=\sqrt{10000*4902}=\sqrt{10000}*\sqrt{4902}=100\sqrt{4902}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7000)-100\sqrt{4902}}{2*-200}=\frac{7000-100\sqrt{4902}}{-400}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7000)+100\sqrt{4902}}{2*-200}=\frac{7000+100\sqrt{4902}}{-400}
$