(5/6)*r=23/5

Solution for (5/6)*r=23/5 equation:

(5/6)*r=23/5

We move all terms to the left:

(5/6)*r-(23/5)=0


Domain of the equation: 6)*r!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

(+5/6)*r-(+23/5)=0

We multiply parentheses

5r^2-(+23/5)=0

We get rid of parentheses

5r^2-23/5=0

We multiply all the terms by the denominator


5r^2*5-23=0

Wy multiply elements

25r^2-23=0

a = 25; b = 0; c = -23;
Δ = b2-4ac
Δ = 02-4·25·(-23)
Δ = 2300
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2300}=\sqrt{100*23}=\sqrt{100}*\sqrt{23}=10\sqrt{23}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{23}}{2*25}=\frac{0-10\sqrt{23}}{50}
=-\frac{10\sqrt{23}}{50}
=-\frac{\sqrt{23}}{5}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{23}}{2*25}=\frac{0+10\sqrt{23}}{50}
=\frac{10\sqrt{23}}{50}
=\frac{\sqrt{23}}{5}
$