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

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

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

We move all terms to the left:

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


Domain of the equation: 5m!=0

m!=0/5

m!=0

m∈R



Domain of the equation: 3m-4)!=0

m∈R


We get rid of parentheses

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

We calculate fractions


6m/15m^2+(-10m)/15m^2+4=0

We multiply all the terms by the denominator


6m+(-10m)+4*15m^2=0

Wy multiply elements

60m^2+6m+(-10m)=0

We get rid of parentheses

60m^2+6m-10m=0

We add all the numbers together, and all the variables

60m^2-4m=0

a = 60; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·60·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*60}=\frac{0}{120}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*60}=\frac{8}{120}
=1/15
$