Question 174689
{{{n^2-14n+9=-11n-4-5n^2}}} Start with the given equation.



{{{n^2-14n+9+11n+4+5n^2=0}}} Get all terms to the left side.



{{{6n^2-3n+13=0}}} Combine like terms.


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From {{{6n^2-3n+13}}} we can see that {{{a=6}}}, {{{b=-3}}}, and {{{c=13}}}



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



{{{D=(-3)^2-4(6)(13)}}} Plug in {{{a=6}}}, {{{b=-3}}}, and {{{c=13}}}



{{{D=9-4(6)(13)}}} Square {{{-3}}} to get {{{9}}}



{{{D=9-312}}} Multiply {{{4(6)(13)}}} to get {{{(24)(13)=312}}}



{{{D=-303}}} Subtract {{{312}}} from {{{9}}} to get {{{-303}}}



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