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

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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 $

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