How do I solve this math problem; 6+w/15 = w/200 x 50w/250?

Question

I am having a hard time solving this problem on "Planes and Sperical on Electronic Navigation", can you help me solve the problem? The equation is, 6+w/15   =   w/200 x 50w/250?

 

Thank you.

Answer 1

6+w/15=w/200 * 50w/250=w^2/1000.

Multiply through by 3000: 18000+200w=3w^2; 3w^2-200w-18000=0.

w^2-200w/3-6000=0; w^2-200w/3+10000/9-10000/9-6000=0 (completing the square);

(w-100/3)^2=6000+10000/9=(54000+10000)/9=64000/9;

w-100/3=+sqrt(64000)/3=+80sqrt(10)/3; w=100/3+80sqrt(10)/3=117.66 or -50.994.