11x(11x-16)=16

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

11x(11x-16)=16

We move all terms to the left:

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

We multiply parentheses

121x^2-176x-16=0

a = 121; b = -176; c = -16;
Δ = b2-4ac
Δ = -1762-4·121·(-16)
Δ = 38720
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:

$\sqrt{\Delta}=\sqrt{38720}=\sqrt{7744*5}=\sqrt{7744}*\sqrt{5}=88\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-176)-88\sqrt{5}}{2*121}=\frac{176-88\sqrt{5}}{242}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-176)+88\sqrt{5}}{2*121}=\frac{176+88\sqrt{5}}{242}
$