20/m=9-m

Solution for 20/m=9-m equation:

20/m=9-m

We move all terms to the left:

20/m-(9-m)=0


Domain of the equation: m!=0

m∈R


We add all the numbers together, and all the variables

20/m-(-1m+9)=0

We get rid of parentheses

20/m+1m-9=0

We multiply all the terms by the denominator


1m*m-9*m+20=0

We add all the numbers together, and all the variables

-9m+1m*m+20=0

Wy multiply elements

m^2-9m+20=0

a = 1; b = -9; c = +20;
Δ = b2-4ac
Δ = -92-4·1·20
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-1}{2*1}=\frac{8}{2}
=4
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+1}{2*1}=\frac{10}{2}
=5
$