3/m=2m-5

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

3/m=2m-5

We move all terms to the left:

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


Domain of the equation: m!=0

m∈R


We get rid of parentheses

3/m-2m+5=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

5m-2m*m+3=0

Wy multiply elements

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

a = -2; b = 5; c = +3;
Δ = b2-4ac
Δ = 52-4·(-2)·3
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-7}{2*-2}=\frac{-12}{-4}
=+3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+7}{2*-2}=\frac{2}{-4}
=-1/2
$