3/4x-1/3=1+5/6x

Solution for 3/4x-1/3=1+5/6x equation:

3/4x-1/3=1+5/6x

We move all terms to the left:

3/4x-1/3-(1+5/6x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-(5/6x+1)-1/3=0

We get rid of parentheses

3/4x-5/6x-1-1/3=0

We calculate fractions


(-144x^2)/216x^2+162x/216x^2+(-180x)/216x^2-1=0

We multiply all the terms by the denominator


(-144x^2)+162x+(-180x)-1*216x^2=0

Wy multiply elements

(-144x^2)-216x^2+162x+(-180x)=0

We get rid of parentheses

-144x^2-216x^2+162x-180x=0

We add all the numbers together, and all the variables

-360x^2-18x=0

a = -360; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·(-360)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*-360}=\frac{0}{-720}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*-360}=\frac{36}{-720}
=-1/20
$