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)(3)# for #color(red)(a)#
#color(blue)(37)# for #color(blue)(b)#
#color(green)(-7)# for #color(green)(c)# gives:
#x = (-color(blue)(37) +- sqrt(color(blue)(37)^2 - (4 * color(red)(3) * color(green)(-7))))/(2 * color(red)(3))#
#x = (-color(blue)(37) +- sqrt(1369 - (-84)))/6#
#x = (-color(blue)(37) +- sqrt(1369 + 84))/6#
#x = (-color(blue)(37) +- sqrt(1453))/6#
If necessary, we can get to a number as:
#x = (-color(blue)(37) - sqrt(1453))/6# and #x = (-color(blue)(37) + sqrt(1453))/6#
#x = (-color(blue)(37) - 38.118)/6# and #x = (-color(blue)(37) + 38.118)/6#
#x = -75.118/6# and #x = 1.118/6#
#x = -12.520# and #x = 0.186# rounded to the nearest thousandth
