80^3-24m^2+40m-33=0

Solution for 80^3-24m^2+40m-33=0 equation:

80^3-24m^2+40m-33=0

We add all the numbers together, and all the variables

-24m^2+40m+511967=0

a = -24; b = 40; c = +511967;
Δ = b2-4ac
Δ = 402-4·(-24)·511967
Δ = 49150432
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:

$\sqrt{\Delta}=\sqrt{49150432}=\sqrt{16*3071902}=\sqrt{16}*\sqrt{3071902}=4\sqrt{3071902}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{3071902}}{2*-24}=\frac{-40-4\sqrt{3071902}}{-48}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{3071902}}{2*-24}=\frac{-40+4\sqrt{3071902}}{-48}
$