1/2m+3=2m

Solution for 1/2m+3=2m equation:

1/2m+3=2m

We move all terms to the left:

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


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4m^2+6m+1=0

a = -4; b = 6; c = +1;
Δ = b2-4ac
Δ = 62-4·(-4)·1
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*-4}=\frac{-6-2\sqrt{13}}{-8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{13}}{2*-4}=\frac{-6+2\sqrt{13}}{-8}
$