m-5=-4/m

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

m-5=-4/m

We move all terms to the left:

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


Domain of the equation: m)!=0

m!=0/1

m!=0

m∈R


We get rid of parentheses

m+4/m-5=0

We multiply all the terms by the denominator


m*m-5*m+4=0

We add all the numbers together, and all the variables

-5m+m*m+4=0

Wy multiply elements

m^2-5m+4=0

a = 1; b = -5; c = +4;
Δ = b2-4ac
Δ = -52-4·1·4
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3}{2*1}=\frac{2}{2}
=1
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3}{2*1}=\frac{8}{2}
=4
$