50+1/2x=x

Solution for 50+1/2x=x equation:

50+1/2x=x

We move all terms to the left:

50+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+50=0

We multiply all the terms by the denominator


-1x*2x+50*2x+1=0

Wy multiply elements

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

a = -2; b = 100; c = +1;
Δ = b2-4ac
Δ = 1002-4·(-2)·1
Δ = 10008
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:

$\sqrt{\Delta}=\sqrt{10008}=\sqrt{36*278}=\sqrt{36}*\sqrt{278}=6\sqrt{278}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-6\sqrt{278}}{2*-2}=\frac{-100-6\sqrt{278}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+6\sqrt{278}}{2*-2}=\frac{-100+6\sqrt{278}}{-4}
$