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4/3x+3=5/6x
We move all terms to the left:
4/3x+3-(5/6x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 6x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
4/3x-(+5/6x)+3=0
We get rid of parentheses
4/3x-5/6x+3=0
We calculate fractions
24x/18x^2+(-15x)/18x^2+3=0
We multiply all the terms by the denominator
24x+(-15x)+3*18x^2=0
Wy multiply elements
54x^2+24x+(-15x)=0
We get rid of parentheses
54x^2+24x-15x=0
We add all the numbers together, and all the variables
54x^2+9x=0
a = 54; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·54·0
Δ = 81
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{81}=9$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*54}=\frac{-18}{108} =-1/6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*54}=\frac{0}{108} =0 $
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