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9/2x+5=17/x
We move all terms to the left:
9/2x+5-(17/x)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
9/2x-(+17/x)+5=0
We get rid of parentheses
9/2x-17/x+5=0
We calculate fractions
9x/2x^2+(-34x)/2x^2+5=0
We multiply all the terms by the denominator
9x+(-34x)+5*2x^2=0
Wy multiply elements
10x^2+9x+(-34x)=0
We get rid of parentheses
10x^2+9x-34x=0
We add all the numbers together, and all the variables
10x^2-25x=0
a = 10; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·10·0
Δ = 625
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{625}=25$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*10}=\frac{0}{20} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*10}=\frac{50}{20} =2+1/2 $
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