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(9/m+3)+6=2m
We move all terms to the left:
(9/m+3)+6-(2m)=0
Domain of the equation: m+3)!=0We add all the numbers together, and all the variables
m∈R
-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} $
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