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

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

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

We move all terms to the left:

1/3m+5/6m-6-(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-21=0

We calculate fractions


6m/18m^2+15m/18m^2-21=0

We multiply all the terms by the denominator


6m+15m-21*18m^2=0

We add all the numbers together, and all the variables

21m-21*18m^2=0

Wy multiply elements

-378m^2+21m=0

a = -378; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-378)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-378}=\frac{-42}{-756}
=1/18
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-378}=\frac{0}{-756}
=0
$