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3+2/3x=3/4x
We move all terms to the left:
3+2/3x-(3/4x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 4x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
2/3x-(+3/4x)+3=0
We get rid of parentheses
2/3x-3/4x+3=0
We calculate fractions
8x/12x^2+(-9x)/12x^2+3=0
We multiply all the terms by the denominator
8x+(-9x)+3*12x^2=0
Wy multiply elements
36x^2+8x+(-9x)=0
We get rid of parentheses
36x^2+8x-9x=0
We add all the numbers together, and all the variables
36x^2-1x=0
a = 36; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·36·0
Δ = 1
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{1}=1$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*36}=\frac{0}{72} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*36}=\frac{2}{72} =1/36 $
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