1/2m+3-5/6m=-15

Solution for 1/2m+3-5/6m=-15 equation:

1/2m+3-5/6m=-15

We move all terms to the left:

1/2m+3-5/6m-(-15)=0


Domain of the equation: 2m!=0

m!=0/2

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

1/2m-5/6m+18=0

We calculate fractions


6m/12m^2+(-10m)/12m^2+18=0

We multiply all the terms by the denominator


6m+(-10m)+18*12m^2=0

Wy multiply elements

216m^2+6m+(-10m)=0

We get rid of parentheses

216m^2+6m-10m=0

We add all the numbers together, and all the variables

216m^2-4m=0

a = 216; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·216·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*216}=\frac{0}{432}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*216}=\frac{8}{432}
=1/54
$