8-x/2x=1+x/4

Solution for 8-x/2x=1+x/4 equation:

8-x/2x=1+x/4

We move all terms to the left:

8-x/2x-(1+x/4)=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/2x-(x/4+1)+8=0

We get rid of parentheses

-x/2x-x/4-1+8=0

We calculate fractions


(-2x^2)/8x+(-4x)/8x-1+8=0

We add all the numbers together, and all the variables

(-2x^2)/8x+(-4x)/8x+7=0

We multiply all the terms by the denominator


(-2x^2)+(-4x)+7*8x=0

Wy multiply elements

(-2x^2)+(-4x)+56x=0

We get rid of parentheses

-2x^2-4x+56x=0

We add all the numbers together, and all the variables

-2x^2+52x=0

a = -2; b = 52; c = 0;
Δ = b2-4ac
Δ = 522-4·(-2)·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-52}{2*-2}=\frac{-104}{-4}
=+26
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+52}{2*-2}=\frac{0}{-4}
=0
$