3m2+51m-84=-6m2

Solution for 3m2+51m-84=-6m2 equation:

3m^2+51m-84=-6m^2

We move all terms to the left:

3m^2+51m-84-(-6m^2)=0

We get rid of parentheses

3m^2+6m^2+51m-84=0

We add all the numbers together, and all the variables

9m^2+51m-84=0

a = 9; b = 51; c = -84;
Δ = b2-4ac
Δ = 512-4·9·(-84)
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-75}{2*9}=\frac{-126}{18}
=-7
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+75}{2*9}=\frac{24}{18}
=1+1/3
$