3m^2=54+9m

Solution for 3m^2=54+9m equation:

3m^2=54+9m

We move all terms to the left:

3m^2-(54+9m)=0

We add all the numbers together, and all the variables

3m^2-(9m+54)=0

We get rid of parentheses

3m^2-9m-54=0

a = 3; b = -9; c = -54;
Δ = b2-4ac
Δ = -92-4·3·(-54)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-27}{2*3}=\frac{-18}{6}
=-3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+27}{2*3}=\frac{36}{6}
=6
$