3/2r-21/8=3/4r

Solution for 3/2r-21/8=3/4r equation:

3/2r-21/8=3/4r

We move all terms to the left:

3/2r-21/8-(3/4r)=0


Domain of the equation: 2r!=0

r!=0/2

r!=0

r∈R



Domain of the equation: 4r)!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

3/2r-(+3/4r)-21/8=0

We get rid of parentheses

3/2r-3/4r-21/8=0

We calculate fractions


(-672r^2)/512r^2+768r/512r^2+(-384r)/512r^2=0

We multiply all the terms by the denominator


(-672r^2)+768r+(-384r)=0

We get rid of parentheses

-672r^2+768r-384r=0

We add all the numbers together, and all the variables

-672r^2+384r=0

a = -672; b = 384; c = 0;
Δ = b2-4ac
Δ = 3842-4·(-672)·0
Δ = 147456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{147456}=384$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(384)-384}{2*-672}=\frac{-768}{-1344}
=4/7
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(384)+384}{2*-672}=\frac{0}{-1344}
=0
$