#ax*x - bx + c = 0# can be rewritten as:
#ax^2 - bx + c = 0#
We can use the quadratic equation to solve this problem:
The quadratic formula states:
For #color(red)(l)x^2 + color(blue)(m)x + color(green)(n) = 0#, the values of #x# which are the solutions to the equation are given by:
#x = (-color(blue)(m) +- sqrt(color(blue)(m)^2 - (4color(red)(l)color(green)(n))))/(2 * color(red)(l))#
Substituting:
#color(red)(a)# for #color(red)(l)#
#color(blue)(-b)# for #color(blue)(m)#
#color(green)(c)# for #color(green)(n)# gives:
#x = (-color(blue)(-b) +- sqrt(color(blue)(-b)^2 - (4 * color(red)(a) * color(green)(c))))/(2 * color(red)(a))#
Or
#x = (color(blue)(b) +- sqrt(color(blue)(-b)^2 - (4 * color(red)(a) * color(green)(c))))/(2 * color(red)(a))#
