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)(6)# for #color(red)(a)#
#color(blue)(-1)# for #color(blue)(b)#
#color(green)(-12)# for #color(green)(c)# gives:
#a = (-color(blue)((-1)) +- sqrt(color(blue)((-1))^2 - (4 * color(red)(6) * color(green)(-12))))/(2 * color(red)(6))#
#a = (1 +- sqrt(1 - (-288)))/12#
#a = (1 +- sqrt(1 + 288))/12#
#a = (1 +- sqrt(289))/12#
#a = (1 - 17)/12# and #a = (1 + 17)/12#
#a = -16/12# and #a = 18/12#
#a = -(4 xx 4)/(4 xx 3)# and #a = (6 xx 3)/(6 xx 2)#
#a = -(color(red)(cancel(color(black)(4))) xx 4)/(color(red)(cancel(color(black)(4))) xx 3)# and #a = (color(red)(cancel(color(black)(6))) xx 3)/(color(red)(cancel(color(black)(6))) xx 2)#
#a = -4/3# and #a = 3/2#
