2m-19=-24/m

Solution for 2m-19=-24/m equation:

2m-19=-24/m

We move all terms to the left:

2m-19-(-24/m)=0


Domain of the equation: m)!=0

m!=0/1

m!=0

m∈R


We get rid of parentheses

2m+24/m-19=0

We multiply all the terms by the denominator


2m*m-19*m+24=0

We add all the numbers together, and all the variables

-19m+2m*m+24=0

Wy multiply elements

2m^2-19m+24=0

a = 2; b = -19; c = +24;
Δ = b2-4ac
Δ = -192-4·2·24
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-13}{2*2}=\frac{6}{4}
=1+1/2
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+13}{2*2}=\frac{32}{4}
=8
$