We know that the quadratic formula is #(-color(blue)(b)+-sqrt(color(blue)(b)^2-4color(red)(a)color(green)(c)))/(2color(red)(a))#.
All we need to do is extract the values for #color(red)(a), color(blue)(b),# and #color(green)(c)# from the equation.
#color(red)(3)x^2+color(blue)(11)xcolor(green)(-20)#
We can see that:
#color(red)(a)=color(red)(3#
#color(blue)(b)=color(blue)(11#
#color(green)(c)=color(green)(-20#
Now, we can just plug those values into the quadratic formula:
#(-color(blue)(11)+-sqrt(color(blue)(11)^2-4color(red)((3))color(green)((-20))))/(2color(red)((3)))#
#(-11+-sqrt(121+240))/(6)#
#(-11+-sqrt(361))/6#
#(-11+-19)/6#, which is
#(-11+19)/6# and #(-11-19)/6#, which is
#8/6# and #-30/6#, which is
#4/3# and #-5#.
These are the solutions to the equation above.
