Step-by-step explanation:
[tex] {x}^{2} + 3x - 5 = 0[/tex]
a =1. b = 3. c = -5
Quadratic equation
[tex]x = \frac{ - b + \sqrt{ {b}^{2} - 4ac} }{2a} \\ = \frac{ - 3 \: + \sqrt{ {3}^{2} \: - 4(1)( - 5) } }{2} \\ = \frac{ - 3 \: + \: \sqrt{29} }{2} [/tex]
Note: the plus sign in the quadratic equation should read "+-"
Therefore, the roots of the quadratic equation are
[tex]\frac{ - 3 \: + \: \sqrt{29} }{2} \: \: and \: \: \frac{ - 3 \: - \: \sqrt{29} }{2} [/tex]
