m-9/m-3=-1

Solution for m-9/m-3=-1 equation:

m-9/m-3=-1

We move all terms to the left:

m-9/m-3-(-1)=0


Domain of the equation: m!=0

m∈R


We add all the numbers together, and all the variables

m-9/m-2=0

We multiply all the terms by the denominator


m*m-2*m-9=0

We add all the numbers together, and all the variables

-2m+m*m-9=0

Wy multiply elements

m^2-2m-9=0

a = 1; b = -2; c = -9;
Δ = b2-4ac
Δ = -22-4·1·(-9)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{10}}{2*1}=\frac{2-2\sqrt{10}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{10}}{2*1}=\frac{2+2\sqrt{10}}{2}
$