1/m+1/m+1=5/2m+2

Solution for 1/m+1/m+1=5/2m+2 equation:

1/m+1/m+1=5/2m+2

We move all terms to the left:

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


Domain of the equation: m!=0

m∈R



Domain of the equation: 2m+2)!=0

m∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2m^2-3m+1=0

a = -2; b = -3; c = +1;
Δ = b2-4ac
Δ = -32-4·(-2)·1
Δ = 17
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{17}}{2*-2}=\frac{3-\sqrt{17}}{-4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{17}}{2*-2}=\frac{3+\sqrt{17}}{-4}
$