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

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

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

We move all terms to the left:

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


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: 4m+16)!=0

m∈R


We get rid of parentheses

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

We calculate fractions


12m/8m^2+(-2m)/8m^2-16+4=0

We add all the numbers together, and all the variables

12m/8m^2+(-2m)/8m^2-12=0

We multiply all the terms by the denominator


12m+(-2m)-12*8m^2=0

Wy multiply elements

-96m^2+12m+(-2m)=0

We get rid of parentheses

-96m^2+12m-2m=0

We add all the numbers together, and all the variables

-96m^2+10m=0

a = -96; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-96)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-96}=\frac{-20}{-192}
=5/48
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-96}=\frac{0}{-192}
=0
$