4.5r=3.2+4/5r

Solution for 4.5r=3.2+4/5r equation:

4.5r=3.2+4/5r

We move all terms to the left:

4.5r-(3.2+4/5r)=0


Domain of the equation: 5r)!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

4.5r-(4/5r+3.2)=0

We get rid of parentheses

4.5r-4/5r-3.2=0

We multiply all the terms by the denominator


(4.5r)*5r-(3.2)*5r-4=0

We add all the numbers together, and all the variables

(+4.5r)*5r-(3.2)*5r-4=0

We multiply parentheses

20r^2-16r-4=0

a = 20; b = -16; c = -4;
Δ = b2-4ac
Δ = -162-4·20·(-4)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-24}{2*20}=\frac{-8}{40}
=-1/5
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+24}{2*20}=\frac{40}{40}
=1
$