2/3m-3/5m=10

Solution for 2/3m-3/5m=10 equation:

2/3m-3/5m=10

We move all terms to the left:

2/3m-3/5m-(10)=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+(-9m)/15m^2-10=0

We multiply all the terms by the denominator


10m+(-9m)-10*15m^2=0

Wy multiply elements

-150m^2+10m+(-9m)=0

We get rid of parentheses

-150m^2+10m-9m=0

We add all the numbers together, and all the variables

-150m^2+m=0

a = -150; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-150)·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*-150}=\frac{-2}{-300}
=1/150
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-150}=\frac{0}{-300}
=0
$