step by step?

\(((5/2*(2*x-1600)+3)/(sqrt((x^2)-(1600*x)+890000)))=0\\\\ \frac{5/2*(2*x-1600)+3}{\sqrt{x^2-(1600*x)+890000}}=0\\ \mbox{I think that is your question}\\ \mbox{you need to note that the bottom cannot be zero}\\ 5/2*(2*x-1600)+3=0\\ \frac{5}{2}*(2*x-1600)+3=0\\ \frac{5}{2}*(2*x-1600)=-3\\ \frac{5}{\not{2}}*\not{2}(x-800)=-3\\ 5(x-800)=-3\\ x-800=-3/5\\ x-800=-0.6\\ x=800-0.6\\ x=799.4 \)

 

This is the same as our guests answer :)

now you need to check that this does not make the denominator 0

799.4^2-1600*799.4+890000 = about 250,000  so that is ok :)

 

x= 799.4

step by step?

((5/2*(2*x-1600)+3)/(sqrt((x^2)-(1600*x)+890000)))=0

 

Solve for x over the real numbers:
(3+5/2 (2 x-1600))/sqrt(x^2-1600 x+890000) = 0

Split into two equations:
(x^2-1600 x+890000)^(-1/2) = 0 or 3+5/2 (2 x-1600) = 0

Raise both sides to the power of -2:
x^2-1600 x+890000 = 0 or 3+5/2 (2 x-1600) = 0

Subtract 890000 from both sides:
x^2-1600 x = -890000 or 3+5/2 (2 x-1600) = 0

Add 640000 to both sides:
x^2-1600 x+640000 = -250000 or 3+5/2 (2 x-1600) = 0

Write the left hand side as a square:
(x-800)^2 = -250000 or 3+5/2 (2 x-1600) = 0

(x-800)^2 = -250000 has no solution since for all x on the real line, (x-800)^2 >=0 and -250000<0:
3+5/2 (2 x-1600) = 0

Expand out terms of the left hand side:
5 x-3997 = 0

Add 3997 to both sides:
5 x = 3997

Divide both sides by 5:
Answer: | 
| x = 3997/5