(9/m+3)+6=2m

Solution for (9/m+3)+6=2m equation:

(9/m+3)+6=2m

We move all terms to the left:

(9/m+3)+6-(2m)=0


Domain of the equation: m+3)!=0

m∈R


We add all the numbers together, and all the variables

-2m+(9/m+3)+6=0

We get rid of parentheses

-2m+9/m+3+6=0

We multiply all the terms by the denominator


-2m*m+3*m+6*m+9=0

We add all the numbers together, and all the variables

9m-2m*m+9=0

Wy multiply elements

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

a = -2; b = 9; c = +9;
Δ = b2-4ac
Δ = 92-4·(-2)·9
Δ = 153
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{17}}{2*-2}=\frac{-9-3\sqrt{17}}{-4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{17}}{2*-2}=\frac{-9+3\sqrt{17}}{-4}
$