(9/m+4)+4=m

Solution for (9/m+4)+4=m equation:

(9/m+4)+4=m

We move all terms to the left:

(9/m+4)+4-(m)=0


Domain of the equation: m+4)!=0

m∈R


We add all the numbers together, and all the variables

-1m+(9/m+4)+4=0

We get rid of parentheses

-1m+9/m+4+4=0

We multiply all the terms by the denominator


-1m*m+4*m+4*m+9=0

We add all the numbers together, and all the variables

8m-1m*m+9=0

Wy multiply elements

-1m^2+8m+9=0

a = -1; b = 8; c = +9;
Δ = b2-4ac
Δ = 82-4·(-1)·9
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-10}{2*-1}=\frac{-18}{-2}
=+9
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+10}{2*-1}=\frac{2}{-2}
=-1
$