-4x(x-11)=16

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

-4x(x-11)=16

We move all terms to the left:

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

We multiply parentheses

-4x^2+44x-16=0

a = -4; b = 44; c = -16;
Δ = b2-4ac
Δ = 442-4·(-4)·(-16)
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{105}}{2*-4}=\frac{-44-4\sqrt{105}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{105}}{2*-4}=\frac{-44+4\sqrt{105}}{-8}
$