2/3m-4-1/2m=1

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

2/3m-4-1/2m=1

We move all terms to the left:

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


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We add all the numbers together, and all the variables

2/3m-1/2m-5=0

We calculate fractions


4m/6m^2+(-3m)/6m^2-5=0

We multiply all the terms by the denominator


4m+(-3m)-5*6m^2=0

Wy multiply elements

-30m^2+4m+(-3m)=0

We get rid of parentheses

-30m^2+4m-3m=0

We add all the numbers together, and all the variables

-30m^2+m=0

a = -30; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-30)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-30}=\frac{-2}{-60}
=1/30
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-30}=\frac{0}{-60}
=0
$