3/4r-1=1/8r+1

Solution for 3/4r-1=1/8r+1 equation:

3/4r-1=1/8r+1

We move all terms to the left:

3/4r-1-(1/8r+1)=0


Domain of the equation: 4r!=0

r!=0/4

r!=0

r∈R



Domain of the equation: 8r+1)!=0

r∈R


We get rid of parentheses

3/4r-1/8r-1-1=0

We calculate fractions


24r/32r^2+(-4r)/32r^2-1-1=0

We add all the numbers together, and all the variables

24r/32r^2+(-4r)/32r^2-2=0

We multiply all the terms by the denominator


24r+(-4r)-2*32r^2=0

Wy multiply elements

-64r^2+24r+(-4r)=0

We get rid of parentheses

-64r^2+24r-4r=0

We add all the numbers together, and all the variables

-64r^2+20r=0

a = -64; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-64)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-64}=\frac{-40}{-128}
=5/16
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-64}=\frac{0}{-128}
=0
$