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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

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

We calculate fractions


2x/12x^2+30x/12x^2+2=0

We multiply all the terms by the denominator


2x+30x+2*12x^2=0

We add all the numbers together, and all the variables

32x+2*12x^2=0

Wy multiply elements

24x^2+32x=0

a = 24; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·24·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*24}=\frac{-64}{48}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*24}=\frac{0}{48}
=0
$