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1/(3x)-5/(6x)=17
We move all terms to the left:
1/(3x)-5/(6x)-(17)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 6x!=0We calculate fractions
x!=0/6
x!=0
x∈R
6x/18x^2+(-15x)/18x^2-17=0
We multiply all the terms by the denominator
6x+(-15x)-17*18x^2=0
Wy multiply elements
-306x^2+6x+(-15x)=0
We get rid of parentheses
-306x^2+6x-15x=0
We add all the numbers together, and all the variables
-306x^2-9x=0
a = -306; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-306)·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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-306}=\frac{0}{-612} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-306}=\frac{18}{-612} =-1/34 $
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