Solve for $x$, where $x > 0$ and $0 = -21x^2 - 11x + 40.$ Express your answer as a simplified common fraction.

Solve for x:
-21 x^2 - 11 x + 40 = 0

The left hand side factors into a product with three terms:
-(3 x + 5) (7 x - 8) = 0

Multiply both sides by -1:
(3 x + 5) (7 x - 8) = 0

Split into two equations:
3 x + 5 = 0 or 7 x - 8 = 0

Subtract 5 from both sides:
3 x = -5 or 7 x - 8 = 0

Divide both sides by 3:
x = -5/3 or 7 x - 8 = 0

Add 8 to both sides:
x = -5/3 or 7 x = 8

Divide both sides by 7:
 
x = -5/3        or          x = 8/7

Good job but it is supposed to only be 8/7 because x is bigger than 0 so it can not be -5/3.