19x-1/x+17=0

Solution for 19x-1/x+17=0 equation:

19x-1/x+17=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


19x*x+17*x-1=0

We add all the numbers together, and all the variables

17x+19x*x-1=0

Wy multiply elements

19x^2+17x-1=0

a = 19; b = 17; c = -1;
Δ = b2-4ac
Δ = 172-4·19·(-1)
Δ = 365
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{-(17)-\sqrt{365}}{2*19}=\frac{-17-\sqrt{365}}{38}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{365}}{2*19}=\frac{-17+\sqrt{365}}{38}
$