2x⁸⁸ + 3x⁸⁷ − 13x² + 5x + 9 = 0

implies that 2x⁸⁸ + 3x⁸⁷ = 13x² - 5x - 9

or x⁸⁷(2x+3) = 13x² - 5x - 9

now plot the left and right graphs for getting the intersecting points

Hint: Parabola will face in upward direction as a is positive, take x=0 we get -9 so 1 root will be positive and 1 negative,

x⁸⁷(2x+3) will be 0 for x = -3/2 and x = 0 besides it consider some values as x = 1 and -1

You will get one root between 0 and -1 

now check both the graph at x= -2, you will get the idea about the second intersection