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

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

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

We move all terms to the left:

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

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

We calculate fractions


(-12m)/18m^2+(-3m)/18m^2+5=0

We multiply all the terms by the denominator


(-12m)+(-3m)+5*18m^2=0

Wy multiply elements

90m^2+(-12m)+(-3m)=0

We get rid of parentheses

90m^2-12m-3m=0

We add all the numbers together, and all the variables

90m^2-15m=0

a = 90; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·90·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*90}=\frac{0}{180}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*90}=\frac{30}{180}
=1/6
$