4/2x+2=-32/8x

Solution for 4/2x+2=-32/8x equation:

4/2x+2=-32/8x

We move all terms to the left:

4/2x+2-(-32/8x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

4/2x+32/8x+2=0

We calculate fractions


32x/16x^2+64x/16x^2+2=0

We multiply all the terms by the denominator


32x+64x+2*16x^2=0

We add all the numbers together, and all the variables

96x+2*16x^2=0

Wy multiply elements

32x^2+96x=0

a = 32; b = 96; c = 0;
Δ = b2-4ac
Δ = 962-4·32·0
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-96}{2*32}=\frac{-192}{64}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+96}{2*32}=\frac{0}{64}
=0
$