1/4x-1=1/6x+2

Solution for 1/4x-1=1/6x+2 equation:

1/4x-1=1/6x+2

We move all terms to the left:

1/4x-1-(1/6x+2)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



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

x∈R


We get rid of parentheses

1/4x-1/6x-2-1=0

We calculate fractions


6x/24x^2+(-4x)/24x^2-2-1=0

We add all the numbers together, and all the variables

6x/24x^2+(-4x)/24x^2-3=0

We multiply all the terms by the denominator


6x+(-4x)-3*24x^2=0

Wy multiply elements

-72x^2+6x+(-4x)=0

We get rid of parentheses

-72x^2+6x-4x=0

We add all the numbers together, and all the variables

-72x^2+2x=0

a = -72; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-72)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-72}=\frac{-4}{-144}
=1/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-72}=\frac{0}{-144}
=0
$