m=6/m+9

Solution for m=6/m+9 equation:

m=6/m+9

We move all terms to the left:

m-(6/m+9)=0


Domain of the equation: m+9)!=0

m∈R


We get rid of parentheses

m-6/m-9=0

We multiply all the terms by the denominator


m*m-9*m-6=0

We add all the numbers together, and all the variables

-9m+m*m-6=0

Wy multiply elements

m^2-9m-6=0

a = 1; b = -9; c = -6;
Δ = b2-4ac
Δ = -92-4·1·(-6)
Δ = 105
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{-(-9)-\sqrt{105}}{2*1}=\frac{9-\sqrt{105}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{105}}{2*1}=\frac{9+\sqrt{105}}{2}
$