MathNet 1985 — Part 01 Question 27

Find the roots $r_{1}, r_{2}, r_{3}, r_{4}$ of the equation $4x^{4} - a x^{3} + b x^{2} - c x + 5 = 0$, given that they are positive reals satisfying $r_{1}/2 + r_{2}/4 + r_{3}/5 + r_{4}/8 = 1$.