2m-1/19=m/102m

Solution for 2m-1/19=m/102m equation:

2m-1/19=m/102m

We move all terms to the left:

2m-1/19-(m/102m)=0


Domain of the equation: 102m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

2m-(+m/102m)-1/19=0

We get rid of parentheses

2m-m/102m-1/19=0

We calculate fractions


2m+(-19m)/1938m+(-102m)/1938m=0

We multiply all the terms by the denominator


2m*1938m+(-19m)+(-102m)=0

Wy multiply elements

3876m^2+(-19m)+(-102m)=0

We get rid of parentheses

3876m^2-19m-102m=0

We add all the numbers together, and all the variables

3876m^2-121m=0

a = 3876; b = -121; c = 0;
Δ = b2-4ac
Δ = -1212-4·3876·0
Δ = 14641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14641}=121$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-121)-121}{2*3876}=\frac{0}{7752}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-121)+121}{2*3876}=\frac{242}{7752}
=121/3876
$