1/2x=50-x

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

1/2x=50-x

We move all terms to the left:

1/2x-(50-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

1/2x-(-1x+50)=0

We get rid of parentheses

1/2x+1x-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 = 9992
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:

$\sqrt{\Delta}=\sqrt{9992}=\sqrt{4*2498}=\sqrt{4}*\sqrt{2498}=2\sqrt{2498}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-2\sqrt{2498}}{2*2}=\frac{100-2\sqrt{2498}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+2\sqrt{2498}}{2*2}=\frac{100+2\sqrt{2498}}{4}
$