5/x+5=19/4x

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

5/x+5=19/4x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


20x/4x^2+(-19x)/4x^2+5=0

We multiply all the terms by the denominator


20x+(-19x)+5*4x^2=0

Wy multiply elements

20x^2+20x+(-19x)=0

We get rid of parentheses

20x^2+20x-19x=0

We add all the numbers together, and all the variables

20x^2+x=0

a = 20; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·20·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*20}=\frac{-2}{40}
=-1/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*20}=\frac{0}{40}
=0
$