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9x-16/x=5
We move all terms to the left:
9x-16/x-(5)=0
Domain of the equation: x!=0We multiply all the terms by the denominator
x∈R
9x*x-5*x-16=0
We add all the numbers together, and all the variables
-5x+9x*x-16=0
Wy multiply elements
9x^2-5x-16=0
a = 9; b = -5; c = -16;
Δ = b2-4ac
Δ = -52-4·9·(-16)
Δ = 601
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{-(-5)-\sqrt{601}}{2*9}=\frac{5-\sqrt{601}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{601}}{2*9}=\frac{5+\sqrt{601}}{18} $
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