19-2x-1/x=7*

Solution for 19-2x-1/x=7* equation:

19-2x-1/x=7*

We move all terms to the left:

19-2x-1/x-(7*)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-2x-1/x+19-0=0

We add all the numbers together, and all the variables

-2x-1/x+19=0

We multiply all the terms by the denominator


-2x*x+19*x-1=0

We add all the numbers together, and all the variables

19x-2x*x-1=0

Wy multiply elements

-2x^2+19x-1=0

a = -2; b = 19; c = -1;
Δ = b2-4ac
Δ = 192-4·(-2)·(-1)
Δ = 353
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{-(19)-\sqrt{353}}{2*-2}=\frac{-19-\sqrt{353}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{353}}{2*-2}=\frac{-19+\sqrt{353}}{-4}
$