2m^2-4m-9=m

Solution for 2m^2-4m-9=m equation:

2m^2-4m-9=m

We move all terms to the left:

2m^2-4m-9-(m)=0

We add all the numbers together, and all the variables

2m^2-5m-9=0

a = 2; b = -5; c = -9;
Δ = b2-4ac
Δ = -52-4·2·(-9)
Δ = 97
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{-(-5)-\sqrt{97}}{2*2}=\frac{5-\sqrt{97}}{4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{97}}{2*2}=\frac{5+\sqrt{97}}{4}
$