3-1/6x=-1-2/5x

Solution for 3-1/6x=-1-2/5x equation:

3-1/6x=-1-2/5x

We move all terms to the left:

3-1/6x-(-1-2/5x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-1/6x-(-2/5x-1)+3=0

We get rid of parentheses

-1/6x+2/5x+1+3=0

We calculate fractions


(-5x)/30x^2+12x/30x^2+1+3=0

We add all the numbers together, and all the variables

(-5x)/30x^2+12x/30x^2+4=0

We multiply all the terms by the denominator


(-5x)+12x+4*30x^2=0

We add all the numbers together, and all the variables

12x+(-5x)+4*30x^2=0

Wy multiply elements

120x^2+12x+(-5x)=0

We get rid of parentheses

120x^2+12x-5x=0

We add all the numbers together, and all the variables

120x^2+7x=0

a = 120; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·120·0
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*120}=\frac{-14}{240}
=-7/120
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*120}=\frac{0}{240}
=0
$