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9x-1/x+5=4
We move all terms to the left:
9x-1/x+5-(4)=0
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
9x-1/x+1=0
We multiply all the terms by the denominator
9x*x+1*x-1=0
We add all the numbers together, and all the variables
x+9x*x-1=0
Wy multiply elements
9x^2+x-1=0
a = 9; b = 1; c = -1;
Δ = b2-4ac
Δ = 12-4·9·(-1)
Δ = 37
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{37}}{2*9}=\frac{-1-\sqrt{37}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{37}}{2*9}=\frac{-1+\sqrt{37}}{18} $
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