6m^2+84=-54m

Solution for 6m^2+84=-54m equation:

6m^2+84=-54m

We move all terms to the left:

6m^2+84-(-54m)=0

We get rid of parentheses

6m^2+54m+84=0

a = 6; b = 54; c = +84;
Δ = b2-4ac
Δ = 542-4·6·84
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-30}{2*6}=\frac{-84}{12}
=-7
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+30}{2*6}=\frac{-24}{12}
=-2
$