7/8m-2=15/16m+3

Solution for 7/8m-2=15/16m+3 equation:

7/8m-2=15/16m+3

We move all terms to the left:

7/8m-2-(15/16m+3)=0


Domain of the equation: 8m!=0

m!=0/8

m!=0

m∈R



Domain of the equation: 16m+3)!=0

m∈R


We get rid of parentheses

7/8m-15/16m-3-2=0

We calculate fractions


112m/128m^2+(-120m)/128m^2-3-2=0

We add all the numbers together, and all the variables

112m/128m^2+(-120m)/128m^2-5=0

We multiply all the terms by the denominator


112m+(-120m)-5*128m^2=0

Wy multiply elements

-640m^2+112m+(-120m)=0

We get rid of parentheses

-640m^2+112m-120m=0

We add all the numbers together, and all the variables

-640m^2-8m=0

a = -640; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-640)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-640}=\frac{0}{-1280}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-640}=\frac{16}{-1280}
=-1/80
$