M(x)=(2x-6)(x-4)

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

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

We move all terms to the left:

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

We multiply parentheses ..

-((+2M^2-8M-6M+24))+M=0


We calculate terms in parentheses: -((+2M^2-8M-6M+24)), so:

(+2M^2-8M-6M+24)

We get rid of parentheses

2M^2-8M-6M+24

We add all the numbers together, and all the variables

2M^2-14M+24

Back to the equation:

-(2M^2-14M+24)


We add all the numbers together, and all the variables

M-(2M^2-14M+24)=0

We get rid of parentheses

-2M^2+M+14M-24=0

We add all the numbers together, and all the variables

-2M^2+15M-24=0

a = -2; b = 15; c = -24;
Δ = b2-4ac
Δ = 152-4·(-2)·(-24)
Δ = 33
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{-(15)-\sqrt{33}}{2*-2}=\frac{-15-\sqrt{33}}{-4}
$
$M_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{33}}{2*-2}=\frac{-15+\sqrt{33}}{-4}
$