1/5m+12=1/2m+9

Solution for 1/5m+12=1/2m+9 equation:

1/5m+12=1/2m+9

We move all terms to the left:

1/5m+12-(1/2m+9)=0


Domain of the equation: 5m!=0

m!=0/5

m!=0

m∈R



Domain of the equation: 2m+9)!=0

m∈R


We get rid of parentheses

1/5m-1/2m-9+12=0

We calculate fractions


2m/10m^2+(-5m)/10m^2-9+12=0

We add all the numbers together, and all the variables

2m/10m^2+(-5m)/10m^2+3=0

We multiply all the terms by the denominator


2m+(-5m)+3*10m^2=0

Wy multiply elements

30m^2+2m+(-5m)=0

We get rid of parentheses

30m^2+2m-5m=0

We add all the numbers together, and all the variables

30m^2-3m=0

a = 30; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·30·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*30}=\frac{0}{60}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*30}=\frac{6}{60}
=1/10
$