Answer
Two imaginary solutions.
Work Step by Step
Add $-4x+8$ to both sides of the given equation.
$\Rightarrow x^2-4x+8=4x-8-4x+8$
Simplify.
$\Rightarrow x^2-4x+8=0$
The standard form of the quadratic equation
$\Rightarrow a^2+bx+c=0$
By comparing both equations we identify
$a=1,b=-4$ and $c=8$
The discriminant for the standard form is $b^2-4ac$.
Plug all values.
$=(-4)^2-4(1)(8)$
Simplify.
$=16-32$
$=-16$.
The discriminant is a negative number.
Hence, the solutions are two imaginary numbers.
