(x-5)(40-x) = 324

(x-5)(40-x) = 324

 

\((x-5)(40-x) = 324\\ -x^2+40x+5x-200=324\\ -x^2+45x-524=0\\ x^2-45x+524=0\\ \)

factor(524) = 2^2*131

ok there is not going to be any integer factors here. 

so you will need to use the quadratic formula or completing the squares method.

I am going to use the web2.0calc to find the answers

 

x^2-45x+524=0 = {x=-(((sqrt(71)*i-45)/2)), x=((sqrt(71)*i+45)/2)}

 

mmm  There are no real solutions.

because the discriminant, which is the bit under the square root, is negative.

I can check this by putting the original equation into the web 2 calc

 

(x-5)(40-x) = 324 = {x=-(((sqrt(71)*i-45)/2)), x=((sqrt(71)*i+45)/2)}

 

Yep that is the same :)