1/4r-1/2=2-2/3r

Solution for 1/4r-1/2=2-2/3r equation:

1/4r-1/2=2-2/3r

We move all terms to the left:

1/4r-1/2-(2-2/3r)=0


Domain of the equation: 4r!=0

r!=0/4

r!=0

r∈R



Domain of the equation: 3r)!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

1/4r-(-2/3r+2)-1/2=0

We get rid of parentheses

1/4r+2/3r-2-1/2=0

We calculate fractions


(-36r^2)/48r^2+12r/48r^2+32r/48r^2-2=0

We multiply all the terms by the denominator


(-36r^2)+12r+32r-2*48r^2=0

We add all the numbers together, and all the variables

(-36r^2)+44r-2*48r^2=0

Wy multiply elements

(-36r^2)-96r^2+44r=0

We get rid of parentheses

-36r^2-96r^2+44r=0

We add all the numbers together, and all the variables

-132r^2+44r=0

a = -132; b = 44; c = 0;
Δ = b2-4ac
Δ = 442-4·(-132)·0
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-44}{2*-132}=\frac{-88}{-264}
=1/3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+44}{2*-132}=\frac{0}{-264}
=0
$