-11/3m+1/6m=-7

Solution for -11/3m+1/6m=-7 equation:

-11/3m+1/6m=-7

We move all terms to the left:

-11/3m+1/6m-(-7)=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

-11/3m+1/6m+7=0

We calculate fractions


(-66m)/18m^2+3m/18m^2+7=0

We multiply all the terms by the denominator


(-66m)+3m+7*18m^2=0

We add all the numbers together, and all the variables

3m+(-66m)+7*18m^2=0

Wy multiply elements

126m^2+3m+(-66m)=0

We get rid of parentheses

126m^2+3m-66m=0

We add all the numbers together, and all the variables

126m^2-63m=0

a = 126; b = -63; c = 0;
Δ = b2-4ac
Δ = -632-4·126·0
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-63}{2*126}=\frac{0}{252}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+63}{2*126}=\frac{126}{252}
=1/2
$