r-4/5r=6/5r

Solution for r-4/5r=6/5r equation:

r-4/5r=6/5r

We move all terms to the left:

r-4/5r-(6/5r)=0


Domain of the equation: 5r!=0

r!=0/5

r!=0

r∈R



Domain of the equation: 5r)!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

r-4/5r-(+6/5r)=0

We get rid of parentheses

r-4/5r-6/5r=0

We multiply all the terms by the denominator


r*5r-4-6=0

We add all the numbers together, and all the variables

r*5r-10=0

Wy multiply elements

5r^2-10=0

a = 5; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·5·(-10)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{2}}{2*5}=\frac{0-10\sqrt{2}}{10}
=-\frac{10\sqrt{2}}{10}
=-\sqrt{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{2}}{2*5}=\frac{0+10\sqrt{2}}{10}
=\frac{10\sqrt{2}}{10}
=\sqrt{2}
$