2m-3=6/m

Solution for 2m-3=6/m equation:

2m-3=6/m

We move all terms to the left:

2m-3-(6/m)=0


Domain of the equation: m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

2m-(+6/m)-3=0

We get rid of parentheses

2m-6/m-3=0

We multiply all the terms by the denominator


2m*m-3*m-6=0

We add all the numbers together, and all the variables

-3m+2m*m-6=0

Wy multiply elements

2m^2-3m-6=0

a = 2; b = -3; c = -6;
Δ = b2-4ac
Δ = -32-4·2·(-6)
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{57}}{2*2}=\frac{3-\sqrt{57}}{4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{57}}{2*2}=\frac{3+\sqrt{57}}{4}
$