-16x^2+27x+6=x

Solution for -16x^2+27x+6=x equation:

-16x^2+27x+6=x

We move all terms to the left:

-16x^2+27x+6-(x)=0

We add all the numbers together, and all the variables

-16x^2+26x+6=0

a = -16; b = 26; c = +6;
Δ = b2-4ac
Δ = 262-4·(-16)·6
Δ = 1060
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:

$\sqrt{\Delta}=\sqrt{1060}=\sqrt{4*265}=\sqrt{4}*\sqrt{265}=2\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{265}}{2*-16}=\frac{-26-2\sqrt{265}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{265}}{2*-16}=\frac{-26+2\sqrt{265}}{-32}
$