Answer
2 solutions
Work Step by Step
$$ \text{The quadratic formula is given by:}$$ $$ x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$$
$$ \text{Plugging in the given values:}$$
$$a=1, b=7, c=-5$$
$$ x = \frac{-7 \pm \sqrt{7^2-4(1)(-5)}}{2(1)}$$
$$\text{Reducing within the radical gives: } $$
$$ x = \frac{-7 \pm \sqrt{69}}{(2)1}$$
$$ \text {This gives: } $$
$$x=0.653311931459037,-7.65331193145904$$
$$ \text{Thus, there are 2 real number solutions.}$$