M(3-4m)=7+4(8-m2)

Solution for M(3-4m)=7+4(8-m2) equation:

(3-4M)=7+4(8-M2)

We move all terms to the left:

(3-4M)-(7+4(8-M2))=0

We add all the numbers together, and all the variables

-(7+4(-1M^2+8))+(-4M+3)=0

We get rid of parentheses

-(7+4(-1M^2+8))-4M+3=0


We calculate terms in parentheses: -(7+4(-1M^2+8)), so:

7+4(-1M^2+8)

determiningTheFunctionDomain
4(-1M^2+8)+7

We multiply parentheses

-4M^2+32+7

We add all the numbers together, and all the variables

-4M^2+39

Back to the equation:

-(-4M^2+39)


We get rid of parentheses

4M^2-4M-39+3=0

We add all the numbers together, and all the variables

4M^2-4M-36=0

a = 4; b = -4; c = -36;
Δ = b2-4ac
Δ = -42-4·4·(-36)
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$M_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{37}}{2*4}=\frac{4-4\sqrt{37}}{8}
$
$M_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{37}}{2*4}=\frac{4+4\sqrt{37}}{8}
$