\(48T=48{T}^{2}\)
\(48T-48{T}^{2}=0\)
\(-48{T}^{2}+48T=0\)
\({T}^{2}-T=0\)
\({T}^{2}-T+\frac{1}{4}=\frac{1}{4}\)
\({(T-\frac{1}{2})}^{2}=\frac{1}{4}\)
\(T-\frac{1}{2}=±\frac{1}{2}\)
\(T=\frac{1}{2}±\frac{1}{2}\)
\(T=\frac{1}{2}+\frac{1}{2}\)
\(T=\frac{2}{2}\)
\(T=1\)
\(T=\frac{1}{2}-\frac{1}{2}\)
\(T=\frac{0}{2}\)
\(T=0\)
.Nice way to get to the answer. My way of getting to the answer, completing the square, works too, but your way envolves fewer steps which I did not see. I wish I would have thought of it first.