Solving 2 degree polynomial

Can anyone please help me with this

mu = 0.15; SW = 9.5106e+03; Cldeck = -1.8001; gammaw = 9.81; mu1 = 1.3; L=40; W = 12.5; mu2 = 12; sigma1 = 0.5; sigma2 = 1; hb = 10; gd = 1.1; n = 4; gw = 0.388; Z1 = 0.7602*x; Z2 = 0.6497*x

GZ = (mu*(SW-((0.5*Cldeck*gammaw*(mu1+Z1*sigma1).^2*L*W) + (gammaw*(L*((mu2+Z2*sigma2)-hb-gd)*W + (L*gd*gw*n))))))==0;

beta = round(solve(GZ,x),4)

- 0.922 - 4.2175i

- 0.922 + 4.2175i

I am getting imaginary roots for this equation but actually solving this by calculator leads to real roots why so?

actual roots are

-0.922

-0.922

[David Hill]

Verify your equation, GZ is correct. If you simplifiy(GZ), I get:

23937561971005804986039*x^2 +44140442005713908921200*x+1338370076196338394974528/3==0

Solving the above gives the matlab solution.

[Raj Arora]

Hello david Thanks for your prompt reply.

Can you please tell me how you get the above equation from GZ?

[Raj Arora]

on simplify I am getting this

GZ = (93197176391394825*(0.3801*x+ 13/10)^2)/140737488355328 - 478.016775*x + 5703118778359873761/8589934592000000 == 0

and the roots of this equation is again imaginary

23937561971005804986039*x^2 +44140442005713908921200*x+1338370076196338394974528/3==0 same for this

[David Hill]

syms x;
mu = 0.15; SW = 9.5106e+03; Cldeck = -1.8001; gammaw = 9.81; mu1 = 1.3; L=40; W = 12.5;
mu2 = 12; sigma1 = 0.5; sigma2 = 1; hb = 10; gd = 1.1; n = 4; gw = 0.388;
Z1 = 0.7602*x; Z2 = 0.6497*x; 
GZ = (mu*(SW-((0.5*Cldeck*gammaw*(mu1+Z1*sigma1).^2*L*W) +...
    (gammaw*(L*((mu2+Z2*sigma2)-hb-gd)*W + (L*gd*gw*n))))))==0;
simplify(GZ)