3m+5=3/2m-6

Solution for 3m+5=3/2m-6 equation:

3m+5=3/2m-6

We move all terms to the left:

3m+5-(3/2m-6)=0


Domain of the equation: 2m-6)!=0

m∈R


We get rid of parentheses

3m-3/2m+6+5=0

We multiply all the terms by the denominator


3m*2m+6*2m+5*2m-3=0

Wy multiply elements

6m^2+12m+10m-3=0

We add all the numbers together, and all the variables

6m^2+22m-3=0

a = 6; b = 22; c = -3;
Δ = b2-4ac
Δ = 222-4·6·(-3)
Δ = 556
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:

$\sqrt{\Delta}=\sqrt{556}=\sqrt{4*139}=\sqrt{4}*\sqrt{139}=2\sqrt{139}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{139}}{2*6}=\frac{-22-2\sqrt{139}}{12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{139}}{2*6}=\frac{-22+2\sqrt{139}}{12}
$