3/4m+5=1/2m+14

Solution for 3/4m+5=1/2m+14 equation:

3/4m+5=1/2m+14

We move all terms to the left:

3/4m+5-(1/2m+14)=0


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R



Domain of the equation: 2m+14)!=0

m∈R


We get rid of parentheses

3/4m-1/2m-14+5=0

We calculate fractions


6m/8m^2+(-4m)/8m^2-14+5=0

We add all the numbers together, and all the variables

6m/8m^2+(-4m)/8m^2-9=0

We multiply all the terms by the denominator


6m+(-4m)-9*8m^2=0

Wy multiply elements

-72m^2+6m+(-4m)=0

We get rid of parentheses

-72m^2+6m-4m=0

We add all the numbers together, and all the variables

-72m^2+2m=0

a = -72; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-72)·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*-72}=\frac{-4}{-144}
=1/36
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-72}=\frac{0}{-144}
=0
$