7/8m-1/2=3/16m+5

Solution for 7/8m-1/2=3/16m+5 equation:

7/8m-1/2=3/16m+5

We move all terms to the left:

7/8m-1/2-(3/16m+5)=0


Domain of the equation: 8m!=0

m!=0/8

m!=0

m∈R



Domain of the equation: 16m+5)!=0

m∈R


We get rid of parentheses

7/8m-3/16m-5-1/2=0

We calculate fractions


(-128m^2)/512m^2+448m/512m^2+(-96m)/512m^2-5=0

We multiply all the terms by the denominator


(-128m^2)+448m+(-96m)-5*512m^2=0

Wy multiply elements

(-128m^2)-2560m^2+448m+(-96m)=0

We get rid of parentheses

-128m^2-2560m^2+448m-96m=0

We add all the numbers together, and all the variables

-2688m^2+352m=0

a = -2688; b = 352; c = 0;
Δ = b2-4ac
Δ = 3522-4·(-2688)·0
Δ = 123904
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{123904}=352$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(352)-352}{2*-2688}=\frac{-704}{-5376}
=11/84
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(352)+352}{2*-2688}=\frac{0}{-5376}
=0
$