5/2m+6-1/m+1=1/m+3

Solution for 5/2m+6-1/m+1=1/m+3 equation:

5/2m+6-1/m+1=1/m+3

We move all terms to the left:

5/2m+6-1/m+1-(1/m+3)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: m!=0

m∈R



Domain of the equation: m+3)!=0

m∈R


We add all the numbers together, and all the variables

5/2m-1/m-(1/m+3)+7=0

We get rid of parentheses

5/2m-1/m-1/m-3+7=0

We calculate fractions


5m/2m^2+(-2m-1)/2m^2-3+7=0

We add all the numbers together, and all the variables

5m/2m^2+(-2m-1)/2m^2+4=0

We multiply all the terms by the denominator


5m+(-2m-1)+4*2m^2=0

Wy multiply elements

8m^2+5m+(-2m-1)=0

We get rid of parentheses

8m^2+5m-2m-1=0

We add all the numbers together, and all the variables

8m^2+3m-1=0

a = 8; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·8·(-1)
Δ = 41
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{41}}{2*8}=\frac{-3-\sqrt{41}}{16}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{41}}{2*8}=\frac{-3+\sqrt{41}}{16}
$