m/6m-(5-9m)=12

Solution for m/6m-(5-9m)=12 equation:

m/6m-(5-9m)=12

We move all terms to the left:

m/6m-(5-9m)-(12)=0


Domain of the equation: 6m!=0

m!=0/6

m!=0

m∈R


We add all the numbers together, and all the variables

m/6m-(-9m+5)-12=0

We get rid of parentheses

m/6m+9m-5-12=0

We multiply all the terms by the denominator


m+9m*6m-5*6m-12*6m=0

Wy multiply elements

54m^2+m-30m-72m=0

We add all the numbers together, and all the variables

54m^2-101m=0

a = 54; b = -101; c = 0;
Δ = b2-4ac
Δ = -1012-4·54·0
Δ = 10201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10201}=101$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-101)-101}{2*54}=\frac{0}{108}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-101)+101}{2*54}=\frac{202}{108}
=1+47/54
$