MATLAB: Please, anyone who can handle with the warning message; (Warning: Explicit solution could not be found. > In solve at 169).

explicit solution could not be foundin solve at 169

The problem is getting the solution for the following equations.
4 variables : x y z t
%% Sa=2*pi*30^2*(1-sin10°)+2*pi*t*(30cos10°+(t/2)*tan10°)/cos10°
%% Sb=170^2-pi*(30cos10°+t*tan10°)^2
4 equations:
0.3+x(1+x)-(x^2)/2-z=0
y(1+y)-(y^2)/2-z=0
(170^2)/1.1=Sa/(1+x)+Sb/(1+y)
-0.3*Sa/(1+x)+((Sa*x^2)/(1+x)+(Sb*y^2)/(1+y))/2+z(Sa/(1+x)+Sb/(1+y)-(170^2)/1.1)=0
And this is my code
      syms x real
      syms y real
      syms z real
      syms t real
      Sa=2*pi*30^2*(1-sin(pi/18))+2*pi*t*(30*cos(pi/18)+(t/2)*tan(pi/18))/cos(pi/18);
      Sb=170^2-pi*30^2;
      F=-0.3*Sa/(1+x)+((Sa*x^2)/(1+x)+(Sb*y^2)/(1+y))/2+z*(Sa/(1+x)+Sb/(1+y)-(170^2)/1.1);
      solve('(x^2)/2+x+0.3-z=0','(y^2)/2+y-z=0','(1+x)*((170^2)/(1.1)-(Sb)/(1+y))=Sa','F=0',x, y, z, t)
Warning: Explicit solution could not be found. 
> In solve at 169
ans =
[ empty sym ]
I'm pretty sure that the solution is about x=0.05 y=0.3 z=? t=34

Best Answer

With this code:
syms x y z t real
Sa=2*pi*30^2*(1-sin(pi/18))+2*pi*t*(30*cos(pi/18)+(t/2)*tan(pi/18))/cos(pi/18);
Sa = simplify(Sa, 'steps', 10);
Sb=170^2-pi*30^2;
F=-0.3*Sa/(1+x)+((Sa*x^2)/(1+x)+(Sb*y^2)/(1+y))/2+z*(Sa/(1+x)+Sb/(1+y)-(170^2)/1.1);
F = simplify(F, 'steps',10);
[x,y,z,t] = solve((x^2)/2+x+0.3-z==0, (y^2)/2+y-z==0, (1+x)*((170^2)/(1.1)-(Sb)/(1+y))==Sa, F==0, [x, y, z, t])
and after several minutes (I didn’t time it), I got:
x =
-1.0
y =
-0.22540333075851662296414692004352
z =
-0.2
t =
-26.959447166136052326594445120517
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