x=29+1/2x

Solution for x=29+1/2x equation:

x=29+1/2x

We move all terms to the left:

x-(29+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+29)=0

We get rid of parentheses

x-1/2x-29=0

We multiply all the terms by the denominator


x*2x-29*2x-1=0

Wy multiply elements

2x^2-58x-1=0

a = 2; b = -58; c = -1;
Δ = b2-4ac
Δ = -582-4·2·(-1)
Δ = 3372
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:

$\sqrt{\Delta}=\sqrt{3372}=\sqrt{4*843}=\sqrt{4}*\sqrt{843}=2\sqrt{843}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-2\sqrt{843}}{2*2}=\frac{58-2\sqrt{843}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+2\sqrt{843}}{2*2}=\frac{58+2\sqrt{843}}{4}
$