2/3m-2/5m=4

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

2/3m-2/5m=4

We move all terms to the left:

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


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



Domain of the equation: 5m!=0

m!=0/5

m!=0

m∈R


We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

-60m^2+10m-6m=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{-8}{-120}
=1/15
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-60}=\frac{0}{-120}
=0
$