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

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

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

We move all terms to the left:

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


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: 2m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-1m*2m-3*2m+5-3=0

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -2; b = -6; c = +2;
Δ = b2-4ac
Δ = -62-4·(-2)·2
Δ = 52
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{13}}{2*-2}=\frac{6-2\sqrt{13}}{-4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{13}}{2*-2}=\frac{6+2\sqrt{13}}{-4}
$