4x(9x-11)=16

Solution for 4x(9x-11)=16 equation:

4x(9x-11)=16

We move all terms to the left:

4x(9x-11)-(16)=0

We multiply parentheses

36x^2-44x-16=0

a = 36; b = -44; c = -16;
Δ = b2-4ac
Δ = -442-4·36·(-16)
Δ = 4240
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:

$\sqrt{\Delta}=\sqrt{4240}=\sqrt{16*265}=\sqrt{16}*\sqrt{265}=4\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{265}}{2*36}=\frac{44-4\sqrt{265}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{265}}{2*36}=\frac{44+4\sqrt{265}}{72}
$