First, subtract #color(red)(10)# from each side of the equation to put the equation in standard quadratic for while keeping the equation balanced:
#3x^2 + 13x - color(red)(10) = 10 - color(red)(10)#
#3x^2 + 13x - 10 = 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)(3)# for #color(red)(a)#
#color(blue)(13)# for #color(blue)(b)#
#color(green)(-10)# for #color(green)(c)# gives:
#x = (-color(blue)(13) +- sqrt(color(blue)(13)^2 - (4 * color(red)(3) * color(green)(-10))))/(2 * color(red)(3))#
#x = (-color(blue)(13) +- sqrt(169 - (12 * color(green)(-10))))/6#
#x = (-color(blue)(13) +- sqrt(169 - (-120)))/6#
#x = (-color(blue)(13) +- sqrt(169 + 120))/6#
#x = (-color(blue)(13) +- sqrt(289))/6#
#x = (-color(blue)(13) - 17)/6# and #x = (-color(blue)(13) + 17)/6#
#x = -30/6# and #x = 4/6#
#x = -5# and #x = 2/3#
The Solution Set Is: #x = {-5, 2/3}#
