#0.23x^2+6.5x+4.3<0#
Comparing with standard quadratic equation #ax^2+bx+c=0#
# a= 0.23 ,b=6.5 ,c=4.3# Discriminant # D= b^2-4ac# or
#D ~~ 38.29# If discriminant positive, we get two real solutions,
Quadratic formula: #x= (-b+-sqrtD)/(2a) #or
#x= (-6.5+-sqrt38.29)/(2*0.23) :. x ~~ -27.58 , x ~~ -0.68#
#0.23x^2+6.5x+4.3<0 #or
# f(x)=0.23 (x +27.58)(x+0.68) <0 # .
Critical points are # x ~~ -27.58 , x ~~ -0.68#
Sign chart: When #x< -27.58# sign of #f(x) # is # (-) * (-) = (+) ; > 0#
When # -27.58 < x < -0.68 # sign of #f(x) # is # (+) * (-) = (-) ; < 0#
When #x > -0.68# sign of #f(x) # is # (+) * (+) = (+) ; > 0#
Solution : # -27.58 < x < -0.68 or x| (-27.58,-0.68)#
graph{0.23x^2+6.5x+4.3 [-160, 160, -80, 80]}
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