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9x+1=8/x
We move all terms to the left:
9x+1-(8/x)=0
Domain of the equation: x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
9x-(+8/x)+1=0
We get rid of parentheses
9x-8/x+1=0
We multiply all the terms by the denominator
9x*x+1*x-8=0
We add all the numbers together, and all the variables
x+9x*x-8=0
Wy multiply elements
9x^2+x-8=0
a = 9; b = 1; c = -8;
Δ = b2-4ac
Δ = 12-4·9·(-8)
Δ = 289
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{289}=17$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-17}{2*9}=\frac{-18}{18} =-1 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+17}{2*9}=\frac{16}{18} =8/9 $
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