1/4(24m-32)=-3/4(12m+8)

Solution for 1/4(24m-32)=-3/4(12m+8) equation:

1/4(24m-32)=-3/4(12m+8)

We move all terms to the left:

1/4(24m-32)-(-3/4(12m+8))=0


Domain of the equation: 4(24m-32)!=0

m∈R



Domain of the equation: 4(12m+8))!=0

m∈R


We calculate fractions


(4m1/(4(24m-32)*4(12m+8)))+(-(-12m2)/(4(24m-32)*4(12m+8)))=0


We calculate terms in parentheses: +(4m1/(4(24m-32)*4(12m+8))), so:

4m1/(4(24m-32)*4(12m+8))

We multiply all the terms by the denominator


4m1

We add all the numbers together, and all the variables

4m

Back to the equation:

+(4m)



We calculate terms in parentheses: +(-(-12m2)/(4(24m-32)*4(12m+8))), so:

-(-12m2)/(4(24m-32)*4(12m+8))

We add all the numbers together, and all the variables

-(-12m^2)/(4(24m-32)*4(12m+8))

We multiply all the terms by the denominator


-(-12m^2)

We get rid of parentheses

12m^2

Back to the equation:

+(12m^2)


determiningTheFunctionDomain
12m^2+4m=0

a = 12; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·12·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*12}=\frac{-8}{24}
=-1/3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*12}=\frac{0}{24}
=0
$