Tell the solve( ) function that the max degree of the polynomial is 3 to force explicit solutions for the result:
syms a len
p = (35*len*a)/2 - 6125 - ((2*a - 35)^2*(60*a + 4200))/840
solve(p,a,'MaxDegree',3)
which gives
ans =
((245*len)/12 + 30625/36)/((((8575*len)/24 + 7674625/216)^2 - ((245*len)/12 + 30625/36)^3)^(1/2) - (8575*len)/24 - 7674625/216)^(1/3) + ((((8575*len)/24 + 7674625/216)^2 - ((245*len)/12 + 30625/36)^3)^(1/2) - (8575*len)/24 - 7674625/216)^(1/3) - 35/3
- ((245*len)/12 + 30625/36)/(2*((((8575*len)/24 + 7674625/216)^2 - ((245*len)/12 + 30625/36)^3)^(1/2) - (8575*len)/24 - 7674625/216)^(1/3)) - (3^(1/2)*(((245*len)/12 + 30625/36)/((((8575*len)/24 + 7674625/216)^2 - ((245*len)/12 + 30625/36)^3)^(1/2) - (8575*len)/24 - 7674625/216)^(1/3) - ((((8575*len)/24 + 7674625/216)^2 - ((245*len)/12 + 30625/36)^3)^(1/2) - (8575*len)/24 - 7674625/216)^(1/3))*1i)/2 - ((((8575*len)/24 + 7674625/216)^2 - ((245*len)/12 + 30625/36)^3)^(1/2) - (8575*len)/24 - 7674625/216)^(1/3)/2 - 35/3
- ((245*len)/12 + 30625/36)/(2*((((8575*len)/24 + 7674625/216)^2 - ((245*len)/12 + 30625/36)^3)^(1/2) - (8575*len)/24 - 7674625/216)^(1/3)) + (3^(1/2)*(((245*len)/12 + 30625/36)/((((8575*len)/24 + 7674625/216)^2 - ((245*len)/12 + 30625/36)^3)^(1/2) - (8575*len)/24 - 7674625/216)^(1/3) - ((((8575*len)/24 + 7674625/216)^2 - ((245*len)/12 + 30625/36)^3)^(1/2) - (8575*len)/24 - 7674625/216)^(1/3))*1i)/2 - ((((8575*len)/24 + 7674625/216)^2 - ((245*len)/12 + 30625/36)^3)^(1/2) - (8575*len)/24 - 7674625/216)^(1/3)/2 - 35/3
Best Answer