-3m^2+30m-39=0

Solution for -3m^2+30m-39=0 equation:

-3m^2+30m-39=0

a = -3; b = 30; c = -39;
Δ = b2-4ac
Δ = 302-4·(-3)·(-39)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-12\sqrt{3}}{2*-3}=\frac{-30-12\sqrt{3}}{-6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+12\sqrt{3}}{2*-3}=\frac{-30+12\sqrt{3}}{-6}
$