(F)=(x+0.5)x=16

Solution for (F)=(x+0.5)x=16 equation:

()=(F+0.5)F=16

We move all terms to the left:

()-((F+0.5)F)=0

We add all the numbers together, and all the variables

-((F+0.5)F)=0


We calculate terms in parentheses: -((F+0.5)F), so:

(F+0.5)F

We multiply parentheses

F^2+0.5F

Back to the equation:

-(F^2+0.5F)


We get rid of parentheses

-F^2-0.5F=0

We add all the numbers together, and all the variables

-1F^2-0.5F=0

a = -1; b = -0.5; c = 0;
Δ = b2-4ac
Δ = -0.52-4·(-1)·0
Δ = 0.25
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{-(-0.5)-\sqrt{0.25}}{2*-1}=\frac{0.5-\sqrt{0.25}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.5)+\sqrt{0.25}}{2*-1}=\frac{0.5+\sqrt{0.25}}{-2}
$