3m^2-27m=60

Solution for 3m^2-27m=60 equation:

3m^2-27m=60

We move all terms to the left:

3m^2-27m-(60)=0

a = 3; b = -27; c = -60;
Δ = b2-4ac
Δ = -272-4·3·(-60)
Δ = 1449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1449}=\sqrt{9*161}=\sqrt{9}*\sqrt{161}=3\sqrt{161}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{161}}{2*3}=\frac{27-3\sqrt{161}}{6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{161}}{2*3}=\frac{27+3\sqrt{161}}{6}
$