3/x+2+1/2x+4=-4

Solution for 3/x+2+1/2x+4=-4 equation:

3/x+2+1/2x+4=-4

We move all terms to the left:

3/x+2+1/2x+4-(-4)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3/x+1/2x+10=0

We calculate fractions


6x/2x^2+x/2x^2+10=0

We multiply all the terms by the denominator


6x+x+10*2x^2=0

We add all the numbers together, and all the variables

7x+10*2x^2=0

Wy multiply elements

20x^2+7x=0

a = 20; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·20·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*20}=\frac{-14}{40}
=-7/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*20}=\frac{0}{40}
=0
$