x=2x^2-12x+16

Solution for x=2x^2-12x+16 equation:

x=2x^2-12x+16

We move all terms to the left:

x-(2x^2-12x+16)=0

We get rid of parentheses

-2x^2+x+12x-16=0

We add all the numbers together, and all the variables

-2x^2+13x-16=0

a = -2; b = 13; c = -16;
Δ = b2-4ac
Δ = 132-4·(-2)·(-16)
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{41}}{2*-2}=\frac{-13-\sqrt{41}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{41}}{2*-2}=\frac{-13+\sqrt{41}}{-4}
$