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5/3x-2=2/x+3
We move all terms to the left:
5/3x-2-(2/x+3)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: x+3)!=0We get rid of parentheses
x∈R
5/3x-2/x-3-2=0
We calculate fractions
5x/3x^2+(-6x)/3x^2-3-2=0
We add all the numbers together, and all the variables
5x/3x^2+(-6x)/3x^2-5=0
We multiply all the terms by the denominator
5x+(-6x)-5*3x^2=0
Wy multiply elements
-15x^2+5x+(-6x)=0
We get rid of parentheses
-15x^2+5x-6x=0
We add all the numbers together, and all the variables
-15x^2-1x=0
a = -15; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-15)·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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-15}=\frac{0}{-30} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-15}=\frac{2}{-30} =-1/15 $
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