-(1-2x)/2x=29-6x

Solution for -(1-2x)/2x=29-6x equation:

-(1-2x)/2x=29-6x

We move all terms to the left:

-(1-2x)/2x-(29-6x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-(-2x+1)/2x-(-6x+29)=0

We get rid of parentheses

-(-2x+1)/2x+6x-29=0

We multiply all the terms by the denominator


-(-2x+1)+6x*2x-29*2x=0

Wy multiply elements

12x^2-(-2x+1)-58x=0

We get rid of parentheses

12x^2+2x-58x-1=0

We add all the numbers together, and all the variables

12x^2-56x-1=0

a = 12; b = -56; c = -1;
Δ = b2-4ac
Δ = -562-4·12·(-1)
Δ = 3184
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:

$\sqrt{\Delta}=\sqrt{3184}=\sqrt{16*199}=\sqrt{16}*\sqrt{199}=4\sqrt{199}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-4\sqrt{199}}{2*12}=\frac{56-4\sqrt{199}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+4\sqrt{199}}{2*12}=\frac{56+4\sqrt{199}}{24}
$