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5/x+3=2/3x-4
We move all terms to the left:
5/x+3-(2/3x-4)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 3x-4)!=0We get rid of parentheses
x∈R
5/x-2/3x+4+3=0
We calculate fractions
15x/3x^2+(-2x)/3x^2+4+3=0
We add all the numbers together, and all the variables
15x/3x^2+(-2x)/3x^2+7=0
We multiply all the terms by the denominator
15x+(-2x)+7*3x^2=0
Wy multiply elements
21x^2+15x+(-2x)=0
We get rid of parentheses
21x^2+15x-2x=0
We add all the numbers together, and all the variables
21x^2+13x=0
a = 21; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·21·0
Δ = 169
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{169}=13$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*21}=\frac{-26}{42} =-13/21 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*21}=\frac{0}{42} =0 $
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