Question 176433
I think you mean:  {{{-5x^2 - 3 = 0}}}, rather than {{{-5x^-3=0}}} which is what you wrote.


Add {{{3}}} to both sides:


{{{-5x^2=3}}}


Multiply both sides by {{{-1/5}}}


{{{x^2 = -3/5}}}


Take the square root of both sides


{{{x = sqrt(-3/5)=sqrt((-1)(3/5))=sqrt(-1)*sqrt(3/5)=i*sqrt(3/5)}}} or


{{{x = -sqrt(-3/5)=-sqrt((-1)(3/5))=-sqrt(-1)*sqrt(3/5)=-i*sqrt(3/5)}}} 


Now rationalize the denominator:


{{{i*sqrt(3/5)=i(sqrt(3)/sqrt(5))=i(sqrt(3)/sqrt(5))(sqrt(5)/sqrt(5))=i*sqrt(15)/5}}}


{{{-i*sqrt(3/5)=-i(sqrt(3)/sqrt(5))=-i(sqrt(3)/sqrt(5))(sqrt(5)/sqrt(5))=-i*sqrt(15)/5}}}