13/6m-1/2-5/3m=-3/2

Solution for 13/6m-1/2-5/3m=-3/2 equation:

13/6m-1/2-5/3m=-3/2

We move all terms to the left:

13/6m-1/2-5/3m-(-3/2)=0


Domain of the equation: 6m!=0

m!=0/6

m!=0

m∈R



Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We get rid of parentheses

13/6m-5/3m-1/2+3/2=0

We calculate fractions


156m/72m^2+(-120m)/72m^2+(162m^2-1)/72m^2=0

We multiply all the terms by the denominator


156m+(-120m)+(162m^2-1)=0

We get rid of parentheses

162m^2+156m-120m-1=0

We add all the numbers together, and all the variables

162m^2+36m-1=0

a = 162; b = 36; c = -1;
Δ = b2-4ac
Δ = 362-4·162·(-1)
Δ = 1944
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:

$\sqrt{\Delta}=\sqrt{1944}=\sqrt{324*6}=\sqrt{324}*\sqrt{6}=18\sqrt{6}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-18\sqrt{6}}{2*162}=\frac{-36-18\sqrt{6}}{324}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+18\sqrt{6}}{2*162}=\frac{-36+18\sqrt{6}}{324}
$