(x+1)/2x=x/8

Solution for (x+1)/2x=x/8 equation:

(x+1)/2x=x/8

We move all terms to the left:

(x+1)/2x-(x/8)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

(x+1)/2x-(+x/8)=0

We get rid of parentheses

(x+1)/2x-x/8=0

We calculate fractions


(-2x^2)/16x+(8x+8)/16x=0

We multiply all the terms by the denominator


(-2x^2)+(8x+8)=0

We get rid of parentheses

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

a = -2; b = 8; c = +8;
Δ = b2-4ac
Δ = 82-4·(-2)·8
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{2}}{2*-2}=\frac{-8-8\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{2}}{2*-2}=\frac{-8+8\sqrt{2}}{-4}
$