-3/2m+7/2+2/3m=11/6

Solution for -3/2m+7/2+2/3m=11/6 equation:

-3/2m+7/2+2/3m=11/6

We move all terms to the left:

-3/2m+7/2+2/3m-(11/6)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We add all the numbers together, and all the variables

-3/2m+2/3m+7/2-(+11/6)=0

We get rid of parentheses

-3/2m+2/3m+7/2-11/6=0

We calculate fractions


(-396m^2)/144m^2+(-324m)/144m^2+96m/144m^2+756m/144m^2=0

We multiply all the terms by the denominator


(-396m^2)+(-324m)+96m+756m=0

We add all the numbers together, and all the variables

(-396m^2)+852m+(-324m)=0

We get rid of parentheses

-396m^2+852m-324m=0

We add all the numbers together, and all the variables

-396m^2+528m=0

a = -396; b = 528; c = 0;
Δ = b2-4ac
Δ = 5282-4·(-396)·0
Δ = 278784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{278784}=528$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(528)-528}{2*-396}=\frac{-1056}{-792}
=1+1/3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(528)+528}{2*-396}=\frac{0}{-792}
=0
$