4x/19x+30=1/x

Solution for 4x/19x+30=1/x equation:

4x/19x+30=1/x

We move all terms to the left:

4x/19x+30-(1/x)=0


Domain of the equation: 19x!=0

x!=0/19

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x/19x-(+1/x)+30=0

We get rid of parentheses

4x/19x-1/x+30=0

We calculate fractions


4x^2/19x^2+(-19x)/19x^2+30=0

We multiply all the terms by the denominator


4x^2+(-19x)+30*19x^2=0

Wy multiply elements

4x^2+570x^2+(-19x)=0

We get rid of parentheses

4x^2+570x^2-19x=0

We add all the numbers together, and all the variables

574x^2-19x=0

a = 574; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·574·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*574}=\frac{0}{1148}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*574}=\frac{38}{1148}
=19/574
$