42-3/2r=21-3/4r

Solution for 42-3/2r=21-3/4r equation:

42-3/2r=21-3/4r

We move all terms to the left:

42-3/2r-(21-3/4r)=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)+42=0

We get rid of parentheses

-3/2r+3/4r-21+42=0

We calculate fractions


(-12r)/8r^2+6r/8r^2-21+42=0

We add all the numbers together, and all the variables

(-12r)/8r^2+6r/8r^2+21=0

We multiply all the terms by the denominator


(-12r)+6r+21*8r^2=0

We add all the numbers together, and all the variables

6r+(-12r)+21*8r^2=0

Wy multiply elements

168r^2+6r+(-12r)=0

We get rid of parentheses

168r^2+6r-12r=0

We add all the numbers together, and all the variables

168r^2-6r=0

a = 168; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·168·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*168}=\frac{0}{336}
=0
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*168}=\frac{12}{336}
=1/28
$