3/4m-6=5/6m+2

Solution for 3/4m-6=5/6m+2 equation:

3/4m-6=5/6m+2

We move all terms to the left:

3/4m-6-(5/6m+2)=0


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R



Domain of the equation: 6m+2)!=0

m∈R


We get rid of parentheses

3/4m-5/6m-2-6=0

We calculate fractions


18m/24m^2+(-20m)/24m^2-2-6=0

We add all the numbers together, and all the variables

18m/24m^2+(-20m)/24m^2-8=0

We multiply all the terms by the denominator


18m+(-20m)-8*24m^2=0

Wy multiply elements

-192m^2+18m+(-20m)=0

We get rid of parentheses

-192m^2+18m-20m=0

We add all the numbers together, and all the variables

-192m^2-2m=0

a = -192; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-192)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-192}=\frac{0}{-384}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-192}=\frac{4}{-384}
=-1/96
$