-8x=16x^2-27

Solution for -8x=16x^2-27 equation:

-8x=16x^2-27

We move all terms to the left:

-8x-(16x^2-27)=0

We get rid of parentheses

-16x^2-8x+27=0

a = -16; b = -8; c = +27;
Δ = b2-4ac
Δ = -82-4·(-16)·27
Δ = 1792
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:

$\sqrt{\Delta}=\sqrt{1792}=\sqrt{256*7}=\sqrt{256}*\sqrt{7}=16\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-16\sqrt{7}}{2*-16}=\frac{8-16\sqrt{7}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+16\sqrt{7}}{2*-16}=\frac{8+16\sqrt{7}}{-32}
$