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6/5x=3/x-2
We move all terms to the left:
6/5x-(3/x-2)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: x-2)!=0We get rid of parentheses
x∈R
6/5x-3/x+2=0
We calculate fractions
6x/5x^2+(-15x)/5x^2+2=0
We multiply all the terms by the denominator
6x+(-15x)+2*5x^2=0
Wy multiply elements
10x^2+6x+(-15x)=0
We get rid of parentheses
10x^2+6x-15x=0
We add all the numbers together, and all the variables
10x^2-9x=0
a = 10; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·10·0
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*10}=\frac{0}{20} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*10}=\frac{18}{20} =9/10 $
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