Solution assignment 09 Equation with fractions

For which value(s) of $p$ does the following equation have no solutions:

$\displaystyle\frac{x+p}{x-1}=2x$

It seems that there is only a fraction in the left-hand side, but this is not the case. We can write:

$\displaystyle\frac{x+p}{x-1}=\displaystyle\frac{2x}{1}$

Cross-multiplication yields:

$x+p=2x^2-2x$

$2x^2-3x-p=0$

This quadratic equation has no solution if its discriminant is less than $0$ is:

$D=9+8p<0$

Thus the equation has no solutions if:

$p<-\displaystyle\frac{9}{8}$