9/2m-5/m=1

Solution for 9/2m-5/m=1 equation:

9/2m-5/m=1

We move all terms to the left:

9/2m-5/m-(1)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: m!=0

m∈R


We calculate fractions


9m/2m^2+(-10m)/2m^2-1=0

We multiply all the terms by the denominator


9m+(-10m)-1*2m^2=0

Wy multiply elements

-2m^2+9m+(-10m)=0

We get rid of parentheses

-2m^2+9m-10m=0

We add all the numbers together, and all the variables

-2m^2-1m=0

a = -2; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-2)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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