Question 923970
{{{ax^2+bx+c=0

you have {{{5x^2+3x+5=0}}} where {{{a=5}}}, {{{b=3}}}, and {{{c=5}}}

we can find roots using quadratic formula {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}  , and the expression used to find the discriminant {{{D}}} is the expression located under the radical in the quadratic formula

 In a quadratic equation, the discriminant helps tell you the number of real solutions to a quadratic equation.  

if {{{b^2-4*a*c>0  }}} there are two real solutions, if the discriminant is a perfect square the roots are rational, otherwise, they are irrational 

if {{{b^2-4*a*c<0  }}}-> no real solutions, two imaginary (complex) solutions

if {{{b^2-4*a*c=0  }}}-> one real solution

{{{D=b^2-4*a*c  }}}

in your case

=> {{{D=3^2-4*5*5  }}} => {{{D=9-100  }}}=> {{{D=-91  }}}


in your case, {{{D<0}}}-> no real solutions, two imaginary (complex) solutions


let's see it on a graph:


{{{ graph( 600, 600, -10, 10, -10, 10, 5x^2+3x+5) }}}