9m=(2m-5)m-9

Solution for 9m=(2m-5)m-9 equation:

9m=(2m-5)m-9

We move all terms to the left:

9m-((2m-5)m-9)=0


We calculate terms in parentheses: -((2m-5)m-9), so:

(2m-5)m-9

We multiply parentheses

2m^2-5m-9

Back to the equation:

-(2m^2-5m-9)


We get rid of parentheses

-2m^2+9m+5m+9=0

We add all the numbers together, and all the variables

-2m^2+14m+9=0

a = -2; b = 14; c = +9;
Δ = b2-4ac
Δ = 142-4·(-2)·9
Δ = 268
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:

$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{67}}{2*-2}=\frac{-14-2\sqrt{67}}{-4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{67}}{2*-2}=\frac{-14+2\sqrt{67}}{-4}
$