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)(1)# for #color(red)(a)#
#color(blue)(-28)# for #color(blue)(b)#
#color(green)(192)# for #color(green)(c)# gives:
#a = (-color(blue)(-28) +- sqrt(color(blue)((-28))^2 - (4 * color(red)(1) * color(green)(192))))/(2 * color(red)(1))#
#a = (color(blue)(28) +- sqrt(color(blue)(784) - 768))/2#
#a = (color(blue)(28) +- sqrt(16))/2#
#a = (color(blue)(28) + 4)/2# and #a = (color(blue)(28) - 4)/2#
#a = 32/2# and #a = 24/2#
#a = 16# and #a = 12#
