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)(-5)# for #color(blue)(b)#
#color(green)(-2)# for #color(green)(c)# gives:
#x = (-color(blue)((-5)) +- sqrt(color(blue)((-5))^2 - (4 * color(red)(1) * color(green)(-2))))/(2 * color(red)(1))#
#x = (color(blue)(5) +- sqrt(color(blue)(25) - (-8)))/2#
#x = (color(blue)(5) +- sqrt(color(blue)(25) + 8))/2#
#x = (color(blue)(5) +- sqrt(33))/2#
