X=50-1/2x

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

X=50-1/2X

We move all terms to the left:

X-(50-1/2X)=0


Domain of the equation: 2X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

X+1/2X-50=0

We multiply all the terms by the denominator


X*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}
$