3m=12-5/2m

Solution for 3m=12-5/2m equation:

3m=12-5/2m

We move all terms to the left:

3m-(12-5/2m)=0


Domain of the equation: 2m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

3m-(-5/2m+12)=0

We get rid of parentheses

3m+5/2m-12=0

We multiply all the terms by the denominator


3m*2m-12*2m+5=0

Wy multiply elements

6m^2-24m+5=0

a = 6; b = -24; c = +5;
Δ = b2-4ac
Δ = -242-4·6·5
Δ = 456
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:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{114}}{2*6}=\frac{24-2\sqrt{114}}{12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{114}}{2*6}=\frac{24+2\sqrt{114}}{12}
$