(6r-1)6r=11

Solution for (6r-1)6r=11 equation:

(6r-1)6r=11

We move all terms to the left:

(6r-1)6r-(11)=0

We multiply parentheses

36r^2-6r-11=0

a = 36; b = -6; c = -11;
Δ = b2-4ac
Δ = -62-4·36·(-11)
Δ = 1620
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:

$\sqrt{\Delta}=\sqrt{1620}=\sqrt{324*5}=\sqrt{324}*\sqrt{5}=18\sqrt{5}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-18\sqrt{5}}{2*36}=\frac{6-18\sqrt{5}}{72}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+18\sqrt{5}}{2*36}=\frac{6+18\sqrt{5}}{72}
$