Question 174885
To find the number of real solutions, we can use the discriminant formula.



From {{{-4j^2+3j-28}}} we can see that {{{a=-4}}}, {{{b=3}}}, and {{{c=-28}}}



{{{D=b^2-4ac}}} Start with the discriminant formula.



{{{D=(3)^2-4(-4)(-28)}}} Plug in {{{a=-4}}}, {{{b=3}}}, and {{{c=-28}}}



{{{D=9-4(-4)(-28)}}} Square {{{3}}} to get {{{9}}}



{{{D=9-448}}} Multiply {{{4(-4)(-28)}}} to get {{{(-16)(-28)=448}}}



{{{D=-439}}} Subtract {{{448}}} from {{{9}}} to get {{{-439}}}



Since the discriminant is less than zero, this means that there are two complex solutions. In other words, there are no real solutions.