Find all values of t such that floor(t) = 2t + 5. If you find more than one value, then list the values you find in increasing order, separated by commas.
Write $t = n+x$ where $n$ is $\lfloor t\rfloor$ and $x$ is the fractional part ($0\le x<1$). Given that $\lfloor t\rfloor = 2t+5$. We have
\lfloor n+x \rfloor = 2(n+x)+5 \\
n = 2n+2x+5 \\
n = -5-2x
Since $n$ is an integer, $2x$ must also be an integer. And since $0\le x<1$, we have $0\le 2x < 2$, so $x$ is either 0 or 0.5. When $x=0$, we have $n=-5-2\cdot 0=-5$. When $x=0.5$, we have $n=-5-2\cdot 0.5=-6$. Thus, the possible values of $t$ in increasing order are $-6+.5=-5.5$, $-5+0=-5$.