4+1/3r=r+8

Solution for 4+1/3r=r+8 equation:

4+1/3r=r+8

We move all terms to the left:

4+1/3r-(r+8)=0


Domain of the equation: 3r!=0

r!=0/3

r!=0

r∈R


We get rid of parentheses

1/3r-r-8+4=0

We multiply all the terms by the denominator


-r*3r-8*3r+4*3r+1=0

Wy multiply elements

-3r^2-24r+12r+1=0

We add all the numbers together, and all the variables

-3r^2-12r+1=0

a = -3; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·(-3)·1
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{39}}{2*-3}=\frac{12-2\sqrt{39}}{-6}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{39}}{2*-3}=\frac{12+2\sqrt{39}}{-6}
$