1/2x+2=5-1/6x

Solution for 1/2x+2=5-1/6x equation:

1/2x+2=5-1/6x

We move all terms to the left:

1/2x+2-(5-1/6x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(-1/6x+5)+2=0

We get rid of parentheses

1/2x+1/6x-5+2=0

We calculate fractions


6x/12x^2+2x/12x^2-5+2=0

We add all the numbers together, and all the variables

6x/12x^2+2x/12x^2-3=0

We multiply all the terms by the denominator


6x+2x-3*12x^2=0

We add all the numbers together, and all the variables

8x-3*12x^2=0

Wy multiply elements

-36x^2+8x=0

a = -36; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-36)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-36}=\frac{-16}{-72}
=2/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-36}=\frac{0}{-72}
=0
$