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)(-5)# for #color(red)(a)#
#color(blue)(-3)# for #color(blue)(b)#
#color(green)(8)# for #color(green)(c)# gives:
#x = (-color(blue)(-3) +- sqrt(color(blue)(-3)^2 - (4 * color(red)(-5) * color(green)(8))))/(2 * color(red)(-5))#
#x = (3 +- sqrt(9 - (-160)))/-10#
#x = (3 +- sqrt(9 + 160))/-10#
#x = (3 +- sqrt(169))/-10#
#x = (3 - 13)/-10# and #x = (3 + 13)/-10#
#x = (-10)/-10# and #x = 16/-10#
#x = 1# and #x = -8/5#
