1/2m-21/2=11/4m+2

Solution for 1/2m-21/2=11/4m+2 equation:

1/2m-21/2=11/4m+2

We move all terms to the left:

1/2m-21/2-(11/4m+2)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: 4m+2)!=0

m∈R


We get rid of parentheses

1/2m-11/4m-2-21/2=0

We calculate fractions


4m/32m^2+(-88m)/32m^2+(-84m)/32m^2-2=0

We multiply all the terms by the denominator


4m+(-88m)+(-84m)-2*32m^2=0

Wy multiply elements

-64m^2+4m+(-88m)+(-84m)=0

We get rid of parentheses

-64m^2+4m-88m-84m=0

We add all the numbers together, and all the variables

-64m^2-168m=0

a = -64; b = -168; c = 0;
Δ = b2-4ac
Δ = -1682-4·(-64)·0
Δ = 28224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{28224}=168$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-168)-168}{2*-64}=\frac{0}{-128}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-168)+168}{2*-64}=\frac{336}{-128}
=-2+5/8
$