1/2m-16=3/4m+8

Solution for 1/2m-16=3/4m+8 equation:

1/2m-16=3/4m+8

We move all terms to the left:

1/2m-16-(3/4m+8)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



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

m∈R


We get rid of parentheses

1/2m-3/4m-8-16=0

We calculate fractions


4m/8m^2+(-6m)/8m^2-8-16=0

We add all the numbers together, and all the variables

4m/8m^2+(-6m)/8m^2-24=0

We multiply all the terms by the denominator


4m+(-6m)-24*8m^2=0

Wy multiply elements

-192m^2+4m+(-6m)=0

We get rid of parentheses

-192m^2+4m-6m=0

We add all the numbers together, and all the variables

-192m^2-2m=0

a = -192; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-192)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-192}=\frac{0}{-384}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-192}=\frac{4}{-384}
=-1/96
$