-10/3m-5/3-3/2m=-107/12

Solution for -10/3m-5/3-3/2m=-107/12 equation:

-10/3m-5/3-3/2m=-107/12

We move all terms to the left:

-10/3m-5/3-3/2m-(-107/12)=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 get rid of parentheses

-10/3m-3/2m-5/3+107/12=0

We calculate fractions


3852m^2/648m^2+(-240m)/648m^2+(-972m)/648m^2+(-120m)/648m^2=0

We multiply all the terms by the denominator


3852m^2+(-240m)+(-972m)+(-120m)=0

We get rid of parentheses

3852m^2-240m-972m-120m=0

We add all the numbers together, and all the variables

3852m^2-1332m=0

a = 3852; b = -1332; c = 0;
Δ = b2-4ac
Δ = -13322-4·3852·0
Δ = 1774224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1774224}=1332$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1332)-1332}{2*3852}=\frac{0}{7704}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1332)+1332}{2*3852}=\frac{2664}{7704}
=37/107
$