1/(2-4x)+2x=13

Solution for 1/(2-4x)+2x=13 equation:

1/(2-4x)+2x=13

We move all terms to the left:

1/(2-4x)+2x-(13)=0


Domain of the equation: (2-4x)!=0

We move all terms containing x to the left, all other terms to the right

-4x!=-2

x!=-2/-4

x!=1/2

x∈R


We add all the numbers together, and all the variables

1/(-4x+2)+2x-13=0

We add all the numbers together, and all the variables

2x+1/(-4x+2)-13=0

We multiply all the terms by the denominator


2x*(-4x+2)-13*(-4x+2)+1=0

We multiply parentheses

-8x^2+4x+52x-26+1=0

We add all the numbers together, and all the variables

-8x^2+56x-25=0

a = -8; b = 56; c = -25;
Δ = b2-4ac
Δ = 562-4·(-8)·(-25)
Δ = 2336
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:

$\sqrt{\Delta}=\sqrt{2336}=\sqrt{16*146}=\sqrt{16}*\sqrt{146}=4\sqrt{146}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-4\sqrt{146}}{2*-8}=\frac{-56-4\sqrt{146}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+4\sqrt{146}}{2*-8}=\frac{-56+4\sqrt{146}}{-16}
$