9m^2-24m=2

Solution for 9m^2-24m=2 equation:

9m^2-24m=2

We move all terms to the left:

9m^2-24m-(2)=0

a = 9; b = -24; c = -2;
Δ = b2-4ac
Δ = -242-4·9·(-2)
Δ = 648
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:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-18\sqrt{2}}{2*9}=\frac{24-18\sqrt{2}}{18}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+18\sqrt{2}}{2*9}=\frac{24+18\sqrt{2}}{18}
$