-16x^2+32x=11

Solution for -16x^2+32x=11 equation:

-16x^2+32x=11

We move all terms to the left:

-16x^2+32x-(11)=0

a = -16; b = 32; c = -11;
Δ = b2-4ac
Δ = 322-4·(-16)·(-11)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-8\sqrt{5}}{2*-16}=\frac{-32-8\sqrt{5}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+8\sqrt{5}}{2*-16}=\frac{-32+8\sqrt{5}}{-32}
$