M(m-3)54m=-10

Solution for M(m-3)54m=-10 equation:

(M-3)54M=-10

We move all terms to the left:

(M-3)54M-(-10)=0

We add all the numbers together, and all the variables

(M-3)54M+10=0

We multiply parentheses

54M^2-162M+10=0

a = 54; b = -162; c = +10;
Δ = b2-4ac
Δ = -1622-4·54·10
Δ = 24084
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:

$\sqrt{\Delta}=\sqrt{24084}=\sqrt{36*669}=\sqrt{36}*\sqrt{669}=6\sqrt{669}$
$M_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-162)-6\sqrt{669}}{2*54}=\frac{162-6\sqrt{669}}{108}
$
$M_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-162)+6\sqrt{669}}{2*54}=\frac{162+6\sqrt{669}}{108}
$