Factor out the common term \(2\).
\[\sqrt{2(t+3)}-\sqrt{2t-5}=0\]
Square both sides.
\[4t+1-2\sqrt{2(t+3)(2t-5)}=0\]
Separate terms with roots from terms without roots.
\[-2\sqrt{2(t+3)(2t-5)}=-4t-1\]
Square both sides.
\[8(t+3)(2t-5)=16{t}^{2}+8t+1\]
Expand.
\[16{t}^{2}-40t+48t-120=16{t}^{2}+8t+1\]
Simplify \(16{t}^{2}-40t+48t-120\) to \(16{t}^{2}+8t-120\).
\[16{t}^{2}+8t-120=16{t}^{2}+8t+1\]
Cancel \(16{t}^{2}\) on both sides.
\[8t-120=8t+1\]
Cancel \(8t\) on both sides.
\[-120=1\]
Since \(-120=1\) is false, there is no solution.
[No Solution]
