We can 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)(3)# for #color(red)(a)#
#color(blue)(9)# for #color(blue)(b)#
#color(green)(-7)# for #color(green)(c)# gives:
#h = (-color(blue)(9) +- sqrt(color(blue)(9)^2 - (4 * color(red)(3) * color(green)(-7))))/(2 * color(red)(3))#
#h = (-color(blue)(9) +- sqrt(81 - (-84)))/6#
#h = (-color(blue)(9) +- sqrt(81 + 84))/6#
#h = (-9 +- sqrt(165))/6#
