Step-by-step explanation:
[tex]x^{2} + 3x - 5[/tex]
For any quadratic equation [tex]ax^{2} + bx + c = 0[/tex], the quadratic formula is as follows:
[tex]\frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}[/tex]
From the given quadratic equation, we know that [tex]a = 1[/tex], [tex]b = 3[/tex] and [tex]c = -5[/tex]. Plugging in these values into the quadratic formula gives us the following:
[tex]\frac{-(-3) \pm \sqrt{(3)^{2} - 4(1)(-5)}}{2(1)}[/tex]
[tex]\frac{3 \pm \sqrt{9 + 20}}{2}[/tex]
[tex]\frac{3 \pm \sqrt{29}}{2}[/tex]
