36r^2+2r-11=0

Solution for 36r^2+2r-11=0 equation:

36r^2+2r-11=0

a = 36; b = 2; c = -11;
Δ = b2-4ac
Δ = 22-4·36·(-11)
Δ = 1588
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:

$\sqrt{\Delta}=\sqrt{1588}=\sqrt{4*397}=\sqrt{4}*\sqrt{397}=2\sqrt{397}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{397}}{2*36}=\frac{-2-2\sqrt{397}}{72}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{397}}{2*36}=\frac{-2+2\sqrt{397}}{72}
$