find the largest value of k in the equation kx^2 -5x+3=0 that will make its roots real

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find the largest value of k in the equation kx^2 -5x+3=0 that will make its roots real

Mathematics
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im pretty sure the answer is 2, but i need to show proper work and i usd guess and check which will not earn me credit. any other ways to figure it out?
Use the quadratic formula.
\[\Delta = b^2 - 4.a.c\] \[\Delta = 25 - 12k\] If we want real roots, \[\Delta \ge 0\] So: \[25-12k \ge 0 => k \le 25/12\]

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