x=2x2-4x-16

Solution for x=2x2-4x-16 equation:

x=2x^2-4x-16

We move all terms to the left:

x-(2x^2-4x-16)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2+5x+16=0

a = -2; b = 5; c = +16;
Δ = b2-4ac
Δ = 52-4·(-2)·16
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3\sqrt{17}}{2*-2}=\frac{-5-3\sqrt{17}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3\sqrt{17}}{2*-2}=\frac{-5+3\sqrt{17}}{-4}
$