4m-4-m=1/4m

Solution for 4m-4-m=1/4m equation:

4m-4-m=1/4m

We move all terms to the left:

4m-4-m-(1/4m)=0


Domain of the equation: 4m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

4m-m-(+1/4m)-4=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

3m-1/4m-4=0

We multiply all the terms by the denominator


3m*4m-4*4m-1=0

Wy multiply elements

12m^2-16m-1=0

a = 12; b = -16; c = -1;
Δ = b2-4ac
Δ = -162-4·12·(-1)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{19}}{2*12}=\frac{16-4\sqrt{19}}{24}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{19}}{2*12}=\frac{16+4\sqrt{19}}{24}
$