3/4m-5=2/3m+8

Solution for 3/4m-5=2/3m+8 equation:

3/4m-5=2/3m+8

We move all terms to the left:

3/4m-5-(2/3m+8)=0


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R



Domain of the equation: 3m+8)!=0

m∈R


We get rid of parentheses

3/4m-2/3m-8-5=0

We calculate fractions


9m/12m^2+(-8m)/12m^2-8-5=0

We add all the numbers together, and all the variables

9m/12m^2+(-8m)/12m^2-13=0

We multiply all the terms by the denominator


9m+(-8m)-13*12m^2=0

Wy multiply elements

-156m^2+9m+(-8m)=0

We get rid of parentheses

-156m^2+9m-8m=0

We add all the numbers together, and all the variables

-156m^2+m=0

a = -156; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-156)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-156}=\frac{-2}{-312}
=1/156
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-156}=\frac{0}{-312}
=0
$