First, subtract #color(red)(6.8)# from each side of the equation to put the equation in standard form:
#2.3x^2 - 1.4x - color(red)(6.8) = 6.8 - color(red)(6.8)#
#2.3x^2 - 1.4x - 6.8 = 0#
We can now 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)(2.3)# for #color(red)(a)#
#color(blue)(-1.4)# for #color(blue)(b)#
#color(green)(-6.8)# for #color(green)(c)# gives:
#x = (-color(blue)((-1.4)) +- sqrt(color(blue)((-1.4))^2 - (4 * color(red)(2.3) * color(green)(-6.8))))/(2 * color(red)(2.3))#
#x = (color(blue)(1.4) +- sqrt(color(blue)(1.96) - (-62.56)))/4.6#
#x = (color(blue)(1.4) +- sqrt(color(blue)(1.96) + 62.56))/4.6#
#x = (color(blue)(1.4) +- sqrt(64.52))/4.6#
#x = (color(blue)(1.4) +- sqrt(4 * 16.13))/4.6#
#x = (color(blue)(1.4) +- sqrt(4)sqrt(16.13))/4.6#
#x = (color(blue)(1.4) +- 2sqrt(16.13))/4.6#
#x = (color(blue)(1.4) - 2sqrt(16.13))/4.6# and #x = (color(blue)(1.4) + 2sqrt(16.13))/4.6#
#x = (color(blue)((2 * 0.7)) - 2sqrt(16.13))/(2 * 2.3)# and #x = (color(blue)((2 * 0.7)) + 2sqrt(16.13))/(2 * 2.3)#
#x = (color(blue)(0.7) - sqrt(16.13))/2.3# and #x = (color(blue)(0.7) + sqrt(16.13))/2.3#
