M3-9m2+23m-15=0

Solution for M3-9m2+23m-15=0 equation:

3-9M^2+23M-15=0

We add all the numbers together, and all the variables

-9M^2+23M-12=0

a = -9; b = 23; c = -12;
Δ = b2-4ac
Δ = 232-4·(-9)·(-12)
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$M_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$M_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$M_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-\sqrt{97}}{2*-9}=\frac{-23-\sqrt{97}}{-18}
$
$M_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{97}}{2*-9}=\frac{-23+\sqrt{97}}{-18}
$