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47/5x=2-3/3x
We move all terms to the left:
47/5x-(2-3/3x)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 3x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
47/5x-(-3/3x+2)=0
We get rid of parentheses
47/5x+3/3x-2=0
We calculate fractions
141x/15x^2+15x/15x^2-2=0
We multiply all the terms by the denominator
141x+15x-2*15x^2=0
We add all the numbers together, and all the variables
156x-2*15x^2=0
Wy multiply elements
-30x^2+156x=0
a = -30; b = 156; c = 0;
Δ = b2-4ac
Δ = 1562-4·(-30)·0
Δ = 24336
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{24336}=156$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(156)-156}{2*-30}=\frac{-312}{-60} =5+1/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(156)+156}{2*-30}=\frac{0}{-60} =0 $
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