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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x+2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

8x-5*12x^2=0

Wy multiply elements

-60x^2+8x=0

a = -60; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-60)·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*-60}=\frac{-16}{-120}
=2/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-60}=\frac{0}{-120}
=0
$