First, subtract #color(red)(0.4)# from each side of the equation to put the equation in standard form while keeping the equation balanced:
#2.5x^2 - 2.8x - color(red)(0.4) = 0.4 - color(red)(0.4)#
#2.5x^2 - 2.8x - 0.4 = 0#
Now 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)(2.5)# for #color(red)(a)#
#color(blue)(-2.8)# for #color(blue)(b)#
#color(green)(-0.4)# for #color(green)(c)# gives:
#x = (-color(blue)((-2.8)) +- sqrt(color(blue)((-2.8))^2 - (4 * color(red)(2.5) * color(green)(-0.4))))/(2 * color(red)(2.5))#
#x = (2.8 +- sqrt(7.84 - 4))/5#
#x = (2.8 +- sqrt(3.84 - 4))/5#
