11x^2-8x=16

Solution for 11x^2-8x=16 equation:

11x^2-8x=16

We move all terms to the left:

11x^2-8x-(16)=0

a = 11; b = -8; c = -16;
Δ = b2-4ac
Δ = -82-4·11·(-16)
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-16\sqrt{3}}{2*11}=\frac{8-16\sqrt{3}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+16\sqrt{3}}{2*11}=\frac{8+16\sqrt{3}}{22}
$