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

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

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

We move all terms to the left:

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


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



Domain of the equation: 5m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


10m/15m^2+9m/15m^2-8-4=0

We add all the numbers together, and all the variables

10m/15m^2+9m/15m^2-12=0

We multiply all the terms by the denominator


10m+9m-12*15m^2=0

We add all the numbers together, and all the variables

19m-12*15m^2=0

Wy multiply elements

-180m^2+19m=0

a = -180; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-180)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-180}=\frac{-38}{-360}
=19/180
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-180}=\frac{0}{-360}
=0
$