6m-5-5m+3=4(1+1/4m)

Solution for 6m-5-5m+3=4(1+1/4m) equation:

6m-5-5m+3=4(1+1/4m)

We move all terms to the left:

6m-5-5m+3-(4(1+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

6m-5m-(4(1/4m+1))-5+3=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


m*4m-2*4m+1))-(4(1+1))=0

We add all the numbers together, and all the variables

m*4m-2*4m+1))-(42)=0

We add all the numbers together, and all the variables

m*4m-2*4m=0

Wy multiply elements

4m^2-8m=0

a = 4; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·4·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*4}=\frac{0}{8}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*4}=\frac{16}{8}
=2
$