36x^2-141=11

Solution for 36x^2-141=11 equation:

36x^2-141=11

We move all terms to the left:

36x^2-141-(11)=0

We add all the numbers together, and all the variables

36x^2-152=0

a = 36; b = 0; c = -152;
Δ = b2-4ac
Δ = 02-4·36·(-152)
Δ = 21888
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{21888}=\sqrt{576*38}=\sqrt{576}*\sqrt{38}=24\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{38}}{2*36}=\frac{0-24\sqrt{38}}{72}
=-\frac{24\sqrt{38}}{72}
=-\frac{\sqrt{38}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{38}}{2*36}=\frac{0+24\sqrt{38}}{72}
=\frac{24\sqrt{38}}{72}
=\frac{\sqrt{38}}{3}
$