First, add #color(red)(6w^2)# to each side of the equation to put this equation into standard form while keeping the equation balanced:
#color(red)(6w^2) + w + 5 = color(red)(6w^2) - 6w^2#
#6w^2 + w + 5 = 0#
We can then 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)(6)# for #color(red)(a)#
#color(blue)(1)# for #color(blue)(b)#
#color(green)(5)# for #color(green)(c)# gives:
#x = (-color(blue)(1) +- sqrt(color(blue)(1)^2 - (4 * color(red)(6) * color(green)(5))))/(2 * color(red)(6))#
#x = (-color(blue)(1) +- sqrt(1 - 120))/12#
#x = (-color(blue)(1) +- sqrt(-119))/12#
