1/2m+6=3-2m

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

1/2m+6=3-2m

We move all terms to the left:

1/2m+6-(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

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

We get rid of parentheses

1/2m+2m-3+6=0

We multiply all the terms by the denominator


2m*2m-3*2m+6*2m+1=0

Wy multiply elements

4m^2-6m+12m+1=0

We add all the numbers together, and all the variables

4m^2+6m+1=0

a = 4; b = 6; c = +1;
Δ = b2-4ac
Δ = 62-4·4·1
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{5}}{2*4}=\frac{-6-2\sqrt{5}}{8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{5}}{2*4}=\frac{-6+2\sqrt{5}}{8}
$