9x-1/x+5=4

Solution for 9x-1/x+5=4 equation:

9x-1/x+5=4

We move all terms to the left:

9x-1/x+5-(4)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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}
$