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

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

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

We move all terms to the left:

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


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



Domain of the equation: 5m-5)!=0

m∈R


We get rid of parentheses

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

We calculate fractions


10m/15m^2+(-12m)/15m^2+5+3=0

We add all the numbers together, and all the variables

10m/15m^2+(-12m)/15m^2+8=0

We multiply all the terms by the denominator


10m+(-12m)+8*15m^2=0

Wy multiply elements

120m^2+10m+(-12m)=0

We get rid of parentheses

120m^2+10m-12m=0

We add all the numbers together, and all the variables

120m^2-2m=0

a = 120; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·120·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*120}=\frac{0}{240}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*120}=\frac{4}{240}
=1/60
$