Question

Which are the solutions of x2 = 19x 1

Answer 1

Here you go.

I was sorta unsure how to read the last part in your question but I tried my best to interpret it 

Answer 2

For this case we have the following quadratic equation:

$x ^ 2 = 19x + 1$

Rewriting we have:

$x ^ 2 - 19x - 1 = 0$

Then, using the quadratic formula we have:

$x =\frac{-b+/-\sqrt{b^2-4ac}}{2a}$

Substituting values:

$x =\frac{-(-19)+/-\sqrt{(-19)^2-4(1)(-1)}}{2(1)}$

Rewriting:

$x =\frac{19+/-\sqrt{361+4}}{2}$

$x =\frac{19+/-\sqrt{365}}{2}$

Therefore, the solutions are given by:

$x =\frac{19+\sqrt{365}}{2}$

$x =\frac{19-\sqrt{365}}{2}$

Answer:

The solutions of the equation are:

$x =\frac{19+\sqrt{365}}{2}$

$x =\frac{19-\sqrt{365}}{2}$