3/4x+3-2/3x=2+5/6

Solution for 3/4x+3-2/3x=2+5/6 equation:

3/4x+3-2/3x=2+5/6

We move all terms to the left:

3/4x+3-2/3x-(2+5/6)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-2/3x+3-(5/6+2)=0

We get rid of parentheses

3/4x-2/3x+3-2-5/6=0

We calculate fractions


(-180x^2)/432x^2+324x/432x^2+(-288x)/432x^2+3-2=0

We add all the numbers together, and all the variables

(-180x^2)/432x^2+324x/432x^2+(-288x)/432x^2+1=0

We multiply all the terms by the denominator


(-180x^2)+324x+(-288x)+1*432x^2=0

Wy multiply elements

(-180x^2)+432x^2+324x+(-288x)=0

We get rid of parentheses

-180x^2+432x^2+324x-288x=0

We add all the numbers together, and all the variables

252x^2+36x=0

a = 252; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·252·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*252}=\frac{-72}{504}
=-1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*252}=\frac{0}{504}
=0
$