7/4x+2/3=11/6x

Solution for 7/4x+2/3=11/6x equation:

7/4x+2/3=11/6x

We move all terms to the left:

7/4x+2/3-(11/6x)=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

7/4x-(+11/6x)+2/3=0

We get rid of parentheses

7/4x-11/6x+2/3=0

We calculate fractions


288x^2/216x^2+378x/216x^2+(-396x)/216x^2=0

We multiply all the terms by the denominator


288x^2+378x+(-396x)=0

We get rid of parentheses

288x^2+378x-396x=0

We add all the numbers together, and all the variables

288x^2-18x=0

a = 288; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·288·0
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*288}=\frac{0}{576}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*288}=\frac{36}{576}
=1/16
$