2m^2-27=-3m

Solution for 2m^2-27=-3m equation:

2m^2-27=-3m

We move all terms to the left:

2m^2-27-(-3m)=0

We get rid of parentheses

2m^2+3m-27=0

a = 2; b = 3; c = -27;
Δ = b2-4ac
Δ = 32-4·2·(-27)
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*2}=\frac{-18}{4}
=-4+1/2
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+15}{2*2}=\frac{12}{4}
=3
$