-3/2m-m=4+1/2m

Solution for -3/2m-m=4+1/2m equation:

-3/2m-m=4+1/2m

We move all terms to the left:

-3/2m-m-(4+1/2m)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: 2m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

-3/2m-m-(1/2m+4)=0

We add all the numbers together, and all the variables

-1m-3/2m-(1/2m+4)=0

We get rid of parentheses

-1m-3/2m-1/2m-4=0

We multiply all the terms by the denominator


-1m*2m-4*2m-3-1=0

We add all the numbers together, and all the variables

-1m*2m-4*2m-4=0

Wy multiply elements

-2m^2-8m-4=0

a = -2; b = -8; c = -4;
Δ = b2-4ac
Δ = -82-4·(-2)·(-4)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{2}}{2*-2}=\frac{8-4\sqrt{2}}{-4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{2}}{2*-2}=\frac{8+4\sqrt{2}}{-4}
$