For this case we have that by definition, a quadratic equation is of the form:
[tex]ax ^ 2 + bx + c = 0[/tex]
Its roots are given by:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]
By definition, the discriminant is given by:
[tex]D = b ^ 2-4 (a) (c)[/tex]
According to the given equation we have to:
[tex]a = 5\\b = 3\\c = -5[/tex]
Substituting:
[tex]D = 3 ^ 2-4 (5) (- 5)\\D = 9 + 100\\D = 109[/tex]
Answer:
The discriminant is 109
