3/4m+2=7+1/2m

Solution for 3/4m+2=7+1/2m equation:

3/4m+2=7+1/2m

We move all terms to the left:

3/4m+2-(7+1/2m)=0


Domain of the equation: 4m!=0

m!=0/4

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

3/4m-(1/2m+7)+2=0

We get rid of parentheses

3/4m-1/2m-7+2=0

We calculate fractions


6m/8m^2+(-4m)/8m^2-7+2=0

We add all the numbers together, and all the variables

6m/8m^2+(-4m)/8m^2-5=0

We multiply all the terms by the denominator


6m+(-4m)-5*8m^2=0

Wy multiply elements

-40m^2+6m+(-4m)=0

We get rid of parentheses

-40m^2+6m-4m=0

We add all the numbers together, and all the variables

-40m^2+2m=0

a = -40; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-40)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-40}=\frac{-4}{-80}
=1/20
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-40}=\frac{0}{-80}
=0
$