The roots of quadratic equation $3x^2 - 5x - k = 0$ are $m/3$ and $m + 3$. Find the values of $m$ and $k$ Can someone please help me solve this equation. Please put in your working as well so I can see how to do this because this equation has been driving me crazy for days!

Quadratic equation factorization using values of roots:
$ax^2+bx+c=a(x-x_1)(x-x_2)$
Where $x_1$ and $x_2$ are the roots.
So we get:
$3x^2-5x-k=3(x-\frac{m}{3})(x-m-3)$
$3x^2-5x-k=(3x-m)(x-m-3)$
$3x^2-5x-k=3x^2-3xm-9x-mx+m^2+3m$
$3x^2-5x-k=3x^2-4xm-9x+m^2+3m$
$-5x-k=-4xm-9x+m^2+3m$
$5x+k=4xm+9x-m^2-3m$
$5x+k=(4m+9)x+(-m^2-3m)$
Now by comparing terms, we get:
$\begin{cases}
4m+9=5
\\
-m^2-3m=k
\end{cases}$
$1)\quad 4m+9=5 \\
\hspace{9mm} 4m=-4 \\
\hspace{9mm} m=-1$
$2)\quad -m^2-3m=k \\
\hspace{9mm} -(-1)^2-3\times(-1)=k \\
\hspace{9mm} -1+3=k \\
\hspace{9mm} k=2$
So the answer is:
$\begin{cases}
m=-1 \\
k=2
\end{cases}$
