3m-9=-6m^2

Solution for 3m-9=-6m^2 equation:

3m-9=-6m^2

We move all terms to the left:

3m-9-(-6m^2)=0

We get rid of parentheses

6m^2+3m-9=0

a = 6; b = 3; c = -9;
Δ = b2-4ac
Δ = 32-4·6·(-9)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-15}{2*6}=\frac{-18}{12}
=-1+1/2
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+15}{2*6}=\frac{12}{12}
=1
$