6r^2-72r+192=r

Solution for 6r^2-72r+192=r equation:

6r^2-72r+192=r

We move all terms to the left:

6r^2-72r+192-(r)=0

We add all the numbers together, and all the variables

6r^2-73r+192=0

a = 6; b = -73; c = +192;
Δ = b2-4ac
Δ = -732-4·6·192
Δ = 721
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{-(-73)-\sqrt{721}}{2*6}=\frac{73-\sqrt{721}}{12}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-73)+\sqrt{721}}{2*6}=\frac{73+\sqrt{721}}{12}
$