4m-5=19/m

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

4m-5=19/m

We move all terms to the left:

4m-5-(19/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

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

We get rid of parentheses

4m-19/m-5=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

4m^2-5m-19=0

a = 4; b = -5; c = -19;
Δ = b2-4ac
Δ = -52-4·4·(-19)
Δ = 329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{329}}{2*4}=\frac{5-\sqrt{329}}{8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{329}}{2*4}=\frac{5+\sqrt{329}}{8}
$