1/4x-5=1/6x+1

Solution for 1/4x-5=1/6x+1 equation:

1/4x-5=1/6x+1

We move all terms to the left:

1/4x-5-(1/6x+1)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6x+1)!=0

x∈R


We get rid of parentheses

1/4x-1/6x-1-5=0

We calculate fractions


6x/24x^2+(-4x)/24x^2-1-5=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-144x^2+6x+(-4x)=0

We get rid of parentheses

-144x^2+6x-4x=0

We add all the numbers together, and all the variables

-144x^2+2x=0

a = -144; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-144)·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*-144}=\frac{-4}{-288}
=1/72
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-144}=\frac{0}{-288}
=0
$