(3/5)r=12/25

Solution for (3/5)r=12/25 equation:

(3/5)r=12/25

We move all terms to the left:

(3/5)r-(12/25)=0


Domain of the equation: 5)r!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

(+3/5)r-(+12/25)=0

We multiply parentheses

3r^2-(+12/25)=0

We get rid of parentheses

3r^2-12/25=0

We multiply all the terms by the denominator


3r^2*25-12=0

Wy multiply elements

75r^2-12=0

a = 75; b = 0; c = -12;
Δ = b2-4ac
Δ = 02-4·75·(-12)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60}{2*75}=\frac{-60}{150}
=-2/5
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60}{2*75}=\frac{60}{150}
=2/5
$