4+1/5r=r-8

Solution for 4+1/5r=r-8 equation:

4+1/5r=r-8

We move all terms to the left:

4+1/5r-(r-8)=0


Domain of the equation: 5r!=0

r!=0/5

r!=0

r∈R


We get rid of parentheses

1/5r-r+8+4=0

We multiply all the terms by the denominator


-r*5r+8*5r+4*5r+1=0

Wy multiply elements

-5r^2+40r+20r+1=0

We add all the numbers together, and all the variables

-5r^2+60r+1=0

a = -5; b = 60; c = +1;
Δ = b2-4ac
Δ = 602-4·(-5)·1
Δ = 3620
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:

$\sqrt{\Delta}=\sqrt{3620}=\sqrt{4*905}=\sqrt{4}*\sqrt{905}=2\sqrt{905}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{905}}{2*-5}=\frac{-60-2\sqrt{905}}{-10}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{905}}{2*-5}=\frac{-60+2\sqrt{905}}{-10}
$