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 get rid of parentheses

8/4x-x-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 = 16512
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:

$\sqrt{\Delta}=\sqrt{16512}=\sqrt{64*258}=\sqrt{64}*\sqrt{258}=8\sqrt{258}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-8\sqrt{258}}{2*-4}=\frac{128-8\sqrt{258}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+8\sqrt{258}}{2*-4}=\frac{128+8\sqrt{258}}{-8}
$