(1)/(3)m+3-(5)/(6)m=-15

Solution for (1)/(3)m+3-(5)/(6)m=-15 equation:

(1)/(3)m+3-(5)/(6)m=-15

We move all terms to the left:

(1)/(3)m+3-(5)/(6)m-(-15)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



Domain of the equation: 6m!=0

m!=0/6

m!=0

m∈R


We add all the numbers together, and all the variables

1/3m-5/6m+18=0

We calculate fractions


6m/18m^2+(-15m)/18m^2+18=0

We multiply all the terms by the denominator


6m+(-15m)+18*18m^2=0

Wy multiply elements

324m^2+6m+(-15m)=0

We get rid of parentheses

324m^2+6m-15m=0

We add all the numbers together, and all the variables

324m^2-9m=0

a = 324; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·324·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*324}=\frac{0}{648}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*324}=\frac{18}{648}
=1/36
$