6m-3/2m=-3

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

6m-3/2m=-3

We move all terms to the left:

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


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We add all the numbers together, and all the variables

6m-3/2m+3=0

We multiply all the terms by the denominator


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

Wy multiply elements

12m^2+6m-3=0

a = 12; b = 6; c = -3;
Δ = b2-4ac
Δ = 62-4·12·(-3)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{5}}{2*12}=\frac{-6-6\sqrt{5}}{24}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{5}}{2*12}=\frac{-6+6\sqrt{5}}{24}
$