m-3=4m/5m-2

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

m-3=4m/5m-2

We move all terms to the left:

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


Domain of the equation: 5m-2)!=0

m∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

5m^2-4m+10m-15m=0

We add all the numbers together, and all the variables

5m^2-9m=0

a = 5; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·5·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*5}=\frac{0}{10}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*5}=\frac{18}{10}
=1+4/5
$