100+1/2x=x

Solution for 100+1/2x=x equation:

100+1/2x=x

We move all terms to the left:

100+1/2x-(x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+1/2x+100=0

We multiply all the terms by the denominator


-1x*2x+100*2x+1=0

Wy multiply elements

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

a = -2; b = 200; c = +1;
Δ = b2-4ac
Δ = 2002-4·(-2)·1
Δ = 40008
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:

$\sqrt{\Delta}=\sqrt{40008}=\sqrt{4*10002}=\sqrt{4}*\sqrt{10002}=2\sqrt{10002}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-2\sqrt{10002}}{2*-2}=\frac{-200-2\sqrt{10002}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+2\sqrt{10002}}{2*-2}=\frac{-200+2\sqrt{10002}}{-4}
$