(4/9)r=81/16

Solution for (4/9)r=81/16 equation:

(4/9)r=81/16

We move all terms to the left:

(4/9)r-(81/16)=0


Domain of the equation: 9)r!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

(+4/9)r-(+81/16)=0

We multiply parentheses

4r^2-(+81/16)=0

We get rid of parentheses

4r^2-81/16=0

We multiply all the terms by the denominator


4r^2*16-81=0

Wy multiply elements

64r^2-81=0

a = 64; b = 0; c = -81;
Δ = b2-4ac
Δ = 02-4·64·(-81)
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-144}{2*64}=\frac{-144}{128}
=-1+1/8
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+144}{2*64}=\frac{144}{128}
=1+1/8
$