M=4x(2x+6)

Solution for M=4x(2x+6) equation:

=4M(2M+6)

We move all terms to the left:

-(4M(2M+6))=0


We calculate terms in parentheses: -(4M(2M+6)), so:

4M(2M+6)

We multiply parentheses

8M^2+24M

Back to the equation:

-(8M^2+24M)


We get rid of parentheses

-8M^2-24M=0

a = -8; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·(-8)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$M_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$M_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$M_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*-8}=\frac{0}{-16}
=0
$
$M_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*-8}=\frac{48}{-16}
=-3
$