2/3m+2=7-1/2m

Solution for 2/3m+2=7-1/2m equation:

2/3m+2=7-1/2m

We move all terms to the left:

2/3m+2-(7-1/2m)=0


Domain of the equation: 3m!=0

m!=0/3

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

2/3m-(-1/2m+7)+2=0

We get rid of parentheses

2/3m+1/2m-7+2=0

We calculate fractions


4m/6m^2+3m/6m^2-7+2=0

We add all the numbers together, and all the variables

4m/6m^2+3m/6m^2-5=0

We multiply all the terms by the denominator


4m+3m-5*6m^2=0

We add all the numbers together, and all the variables

7m-5*6m^2=0

Wy multiply elements

-30m^2+7m=0

a = -30; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-30)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-30}=\frac{-14}{-60}
=7/30
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-30}=\frac{0}{-60}
=0
$