3/m+5/2m=5

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

3/m+5/2m=5

We move all terms to the left:

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


Domain of the equation: m!=0

m∈R



Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We calculate fractions


6m/2m^2+5m/2m^2-5=0

We multiply all the terms by the denominator


6m+5m-5*2m^2=0

We add all the numbers together, and all the variables

11m-5*2m^2=0

Wy multiply elements

-10m^2+11m=0

a = -10; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-10)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-10}=\frac{-22}{-20}
=1+1/10
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-10}=\frac{0}{-20}
=0
$