5x-19=4/x

Solution for 5x-19=4/x equation:

5x-19=4/x

We move all terms to the left:

5x-19-(4/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-(+4/x)-19=0

We get rid of parentheses

5x-4/x-19=0

We multiply all the terms by the denominator


5x*x-19*x-4=0

We add all the numbers together, and all the variables

-19x+5x*x-4=0

Wy multiply elements

5x^2-19x-4=0

a = 5; b = -19; c = -4;
Δ = b2-4ac
Δ = -192-4·5·(-4)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-21}{2*5}=\frac{-2}{10}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+21}{2*5}=\frac{40}{10}
=4
$