5m+19=4/m

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

5m+19=4/m

We move all terms to the left:

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


Domain of the equation: m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

5m-4/m+19=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

19m+5m*m-4=0

Wy multiply elements

5m^2+19m-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:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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