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

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

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

We move all terms to the left:

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


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

We move all terms containing m to the left, all other terms to the right

m!=2

m∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


-2m*(m-2)+(3m-5)=0

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2m^2+7m-5=0

a = -2; b = 7; c = -5;
Δ = b2-4ac
Δ = 72-4·(-2)·(-5)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3}{2*-2}=\frac{-10}{-4}
=2+1/2
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3}{2*-2}=\frac{-4}{-4}
=1
$