Solve the following quadratic equation using the quadratic formula.

write the solutions in the following form, where r, s, and t are integers, and the fractions are in simplest form.

5x ^ 2 - 8x + 5 = 0
 For this case, the first thing we must do is apply the resolver.
 We have then:
 x = (- b +/- root (b ^ 2 - 4 * a * c)) / (2 * a)
 substituting we have:
 x = (- (- 8) +/- root ((- 8) ^ 2 - 4 * (5) * (5))) / (2 * (5))
 Rewriting:
 x = (8 +/- root (64 - 100)) / (10)
 x = (8 +/- root (-36)) / (10)
 x = (8 +/- 6raiz (-1)) / (10)
 x = (4 +/- 3 * i) / (5)
 
 The solutions are:
 x1 = (4 + 3 * i) / (5)
 x2 = (4 - 3 * i) / (5)