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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


18x/24x^2+(-4x)/24x^2-3-1=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-96x^2+18x+(-4x)=0

We get rid of parentheses

-96x^2+18x-4x=0

We add all the numbers together, and all the variables

-96x^2+14x=0

a = -96; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-96)·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*-96}=\frac{-28}{-192}
=7/48
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-96}=\frac{0}{-192}
=0
$