Answer:
[tex]\boxed{15}[/tex]
Step-by-step explanation:
Set the output equal to 0.
[tex]-2x^2 +20x+150=0[/tex]
Factor left side of the equation.
[tex]-2(x+5)(x-15)=0[/tex]
Set factors equal to 0.
First possibility:
[tex]-2(x+5)=0\\x+5=0\\x=-5[/tex]
Second possibility:
[tex]x-15=0\\x=15[/tex]
The value or prize cannot be negative.
[tex]x\neq -5\\ x=15[/tex]
