how to solve this
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Write the inequality as
x²-5x+15 < 0
Complete the square:
(x-2.5)²+8.75 < 0
The left-hand side is always positive, so the inequality has no solution (∅).
Adding to Andre's answer:
The polynomial x2 -5x +15 is a quadratic and represents a parabola that opens upward and vertex at (2.5, 8.75). This parabola does cross the x axis, so at no point is y < 0
You are going to proceed as if the < is an = sign, with one exception. If you multiply or divide both sides by a negative number, then < has to be reversed to >.
Let's subtract 5x from both sides...
We can go further, and subtract 15 from both sides...
We can multiply both sides by -1...
We can factor...