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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x-2)!=0

x∈R


We get rid of parentheses

1/2x+1/4x+2+4=0

We calculate fractions


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

We add all the numbers together, and all the variables

4x/8x^2+2x/8x^2+6=0

We multiply all the terms by the denominator


4x+2x+6*8x^2=0

We add all the numbers together, and all the variables

6x+6*8x^2=0

Wy multiply elements

48x^2+6x=0

a = 48; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·48·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*48}=\frac{-12}{96}
=-1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*48}=\frac{0}{96}
=0
$