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

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

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

We move all terms to the left:

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


Domain of the equation: 8r!=0

r!=0/8

r!=0

r∈R



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

r∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2688r^2+352r=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:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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