First, rewrite the equation as:

#4x^2 - 9x + 0 = 0#

We can now use the quadratic equation to solve this problem:

The quadratic formula states:

For #color(red)(a)x^2 + color(blue)(b)x + color(green)(c) = 0#, the values of #x# which are the solutions to the equation are given by:

#x = (-color(blue)(b) +- sqrt(color(blue)(b)^2 - (4color(red)(a)color(green)(c))))/(2 * color(red)(a))#

Substituting:

#color(red)(4)# for #color(red)(a)#

#color(blue)(-9)# for #color(blue)(b)#

#color(green)(0)# for #color(green)(c)# gives:

#x = (-color(blue)((-9)) +- sqrt(color(blue)((-9))^2 - (4 * color(red)(4) * color(green)(0))))/(2 * color(red)(4))#

#x = (9 +- sqrt(81 - 0))/8#

#x = (9 +- sqrt(81))/8#

#x = (9 - 9)/8# and #x = (9 + 9)/8#

#x = 0/8# and #x = 18/8#

#x = 0# and #x = 9/4#