M=3a(2a+6)

Solution for M=3a(2a+6) equation:

=3M(2M+6)

We move all terms to the left:

-(3M(2M+6))=0


We calculate terms in parentheses: -(3M(2M+6)), so:

3M(2M+6)

We multiply parentheses

6M^2+18M

Back to the equation:

-(6M^2+18M)


We get rid of parentheses

-6M^2-18M=0

a = -6; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·(-6)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$M_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$M_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$M_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*-6}=\frac{0}{-12}
=0
$
$M_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*-6}=\frac{36}{-12}
=-3
$