3/4m-5-1/2m=12

Solution for 3/4m-5-1/2m=12 equation:

3/4m-5-1/2m=12

We move all terms to the left:

3/4m-5-1/2m-(12)=0


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R



Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We add all the numbers together, and all the variables

3/4m-1/2m-17=0

We calculate fractions


6m/8m^2+(-4m)/8m^2-17=0

We multiply all the terms by the denominator


6m+(-4m)-17*8m^2=0

Wy multiply elements

-136m^2+6m+(-4m)=0

We get rid of parentheses

-136m^2+6m-4m=0

We add all the numbers together, and all the variables

-136m^2+2m=0

a = -136; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-136)·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*-136}=\frac{-4}{-272}
=1/68
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-136}=\frac{0}{-272}
=0
$