# What are the exact solutions of x^2 − 5x − 7 = 0?

$y = {x}^{2} - 5 x - 7 = 0$
$D = {d}^{2} = {b}^{2} - 4 a c = 25 + 28 = 53 \to d = \pm s q r 53$
$x = - \frac{b}{2 a} \pm \frac{d}{2 a} = \frac{5}{2} \pm \frac{s q r 53}{2}$ = $\frac{5 + s q r 53}{2}$