1/6x=3/4x+1

Solution for 1/6x=3/4x+1 equation:

1/6x=3/4x+1

We move all terms to the left:

1/6x-(3/4x+1)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 4x+1)!=0

x∈R


We get rid of parentheses

1/6x-3/4x-1=0

We calculate fractions


4x/24x^2+(-18x)/24x^2-1=0

We multiply all the terms by the denominator


4x+(-18x)-1*24x^2=0

Wy multiply elements

-24x^2+4x+(-18x)=0

We get rid of parentheses

-24x^2+4x-18x=0

We add all the numbers together, and all the variables

-24x^2-14x=0

a = -24; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·(-24)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*-24}=\frac{0}{-48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*-24}=\frac{28}{-48}
=-7/12
$