F(x)=(50,000-2,500x)(15+x)

Solution for F(x)=(50,000-2,500x)(15+x) equation:

(F)=(50.000-2.500F)(15+F)

We move all terms to the left:

(F)-((50.000-2.500F)(15+F))=0

We add all the numbers together, and all the variables

F-((-2.5F+50)(F+15))=0

We multiply parentheses ..

-((-2F^2-30F+50F+750))+F=0


We calculate terms in parentheses: -((-2F^2-30F+50F+750)), so:

(-2F^2-30F+50F+750)

We get rid of parentheses

-2F^2-30F+50F+750

We add all the numbers together, and all the variables

-2F^2+20F+750

Back to the equation:

-(-2F^2+20F+750)


We get rid of parentheses

2F^2-20F+F-750=0

We add all the numbers together, and all the variables

2F^2-19F-750=0

a = 2; b = -19; c = -750;
Δ = b2-4ac
Δ = -192-4·2·(-750)
Δ = 6361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{6361}}{2*2}=\frac{19-\sqrt{6361}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{6361}}{2*2}=\frac{19+\sqrt{6361}}{4}
$