First, we can subtract #color(red)(14)# from each side of the equation to put the equation in standard form while keeping the equation balanced:

#2x^2 + x - color(red)(14) = 14 - color(red)(14)#

#2x^2 + x - 14 = 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)# for #color(red)(a)#

#color(blue)(1)# for #color(blue)(b)#

#color(green)(-14)# for #color(green)(c)# gives:

#x = (-color(blue)(1) +- sqrt(color(blue)(1)^2 - (4 * color(red)(2) * color(green)(-14))))/(2 * color(red)(2))#

#x = (-color(blue)(1) +- sqrt(1 - (-112)))/4#

#x = (-color(blue)(1) +- sqrt(1 + 112))/4#

#x = (-color(blue)(1) - sqrt(1 + 112))/4# and #x = (-color(blue)(1) + sqrt(1 + 112))/4#

#x = (-color(blue)(1) - sqrt(113))/4# and #x = (-color(blue)(1) + sqrt(113))/4#

#x = (-color(blue)(1) - 10.6301)/4# and #x = (-color(blue)(1) + 10.6301)/4#

#x = -11.6301/4# and #x = 9.6301/4#

#x = -2.91# and #x = 2.41# rounded to the nearest hundredth.