1/3m+3-5/m=-15

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

1/3m+3-5/m=-15

We move all terms to the left:

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


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



Domain of the equation: m!=0

m∈R


We add all the numbers together, and all the variables

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

We calculate fractions


m/3m^2+(-15m)/3m^2+18=0

We multiply all the terms by the denominator


m+(-15m)+18*3m^2=0

Wy multiply elements

54m^2+m+(-15m)=0

We get rid of parentheses

54m^2+m-15m=0

We add all the numbers together, and all the variables

54m^2-14m=0

a = 54; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·54·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*54}=\frac{0}{108}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*54}=\frac{28}{108}
=7/27
$