5/2m+6=7/4m-8

Solution for 5/2m+6=7/4m-8 equation:

5/2m+6=7/4m-8

We move all terms to the left:

5/2m+6-(7/4m-8)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: 4m-8)!=0

m∈R


We get rid of parentheses

5/2m-7/4m+8+6=0

We calculate fractions


20m/8m^2+(-14m)/8m^2+8+6=0

We add all the numbers together, and all the variables

20m/8m^2+(-14m)/8m^2+14=0

We multiply all the terms by the denominator


20m+(-14m)+14*8m^2=0

Wy multiply elements

112m^2+20m+(-14m)=0

We get rid of parentheses

112m^2+20m-14m=0

We add all the numbers together, and all the variables

112m^2+6m=0

a = 112; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·112·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*112}=\frac{-12}{224}
=-3/56
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*112}=\frac{0}{224}
=0
$