32/2x=28+8x

Solution for 32/2x=28+8x equation:

32/2x=28+8x

We move all terms to the left:

32/2x-(28+8x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

32/2x-(8x+28)=0

We get rid of parentheses

32/2x-8x-28=0

We multiply all the terms by the denominator


-8x*2x-28*2x+32=0

Wy multiply elements

-16x^2-56x+32=0

a = -16; b = -56; c = +32;
Δ = b2-4ac
Δ = -562-4·(-16)·32
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-72}{2*-16}=\frac{-16}{-32}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+72}{2*-16}=\frac{128}{-32}
=-4
$