r/12=r+6-2r*

Solution for r/12=r+6-2r* equation:

r/12=r+6-2r*

We move all terms to the left:

r/12-(r+6-2r*)=0

We add all the numbers together, and all the variables

r/12-(r-2r*+6)=0

We get rid of parentheses

r/12-r+2r*-6=0

We multiply all the terms by the denominator


r-r*12+(2r*)*12-6*12=0

We add all the numbers together, and all the variables

r-r*12+(+2r*)*12-6*12=0

We add all the numbers together, and all the variables

r-r*12+(+2r*)*12-72=0

We multiply parentheses

24r^2+r-r*12-72=0

Wy multiply elements

24r^2+r-12r-72=0

We add all the numbers together, and all the variables

24r^2-11r-72=0

a = 24; b = -11; c = -72;
Δ = b2-4ac
Δ = -112-4·24·(-72)
Δ = 7033
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{7033}}{2*24}=\frac{11-\sqrt{7033}}{48}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{7033}}{2*24}=\frac{11+\sqrt{7033}}{48}
$