4(2+2x)=32/2x

Solution for 4(2+2x)=32/2x equation:

4(2+2x)=32/2x

We move all terms to the left:

4(2+2x)-(32/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4(2x+2)-(+32/2x)=0

We multiply parentheses

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

We get rid of parentheses

8x-32/2x+8=0

We multiply all the terms by the denominator


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

Wy multiply elements

16x^2+16x-32=0

a = 16; b = 16; c = -32;
Δ = b2-4ac
Δ = 162-4·16·(-32)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-48}{2*16}=\frac{-64}{32}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+48}{2*16}=\frac{32}{32}
=1
$