8/4x+x=32

Solution for 8/4x+x=32 equation:

8/4x+x=32

We move all terms to the left:

8/4x+x-(32)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

x+8/4x-32=0

We multiply all the terms by the denominator


x*4x-32*4x+8=0

Wy multiply elements

4x^2-128x+8=0

a = 4; b = -128; c = +8;
Δ = b2-4ac
Δ = -1282-4·4·8
Δ = 16256
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:

$\sqrt{\Delta}=\sqrt{16256}=\sqrt{64*254}=\sqrt{64}*\sqrt{254}=8\sqrt{254}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-8\sqrt{254}}{2*4}=\frac{128-8\sqrt{254}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+8\sqrt{254}}{2*4}=\frac{128+8\sqrt{254}}{8}
$