800=20x-(1/8)x^2

Solution for 800=20x-(1/8)x^2 equation:

800=20x-(1/8)x^2

We move all terms to the left:

800-(20x-(1/8)x^2)=0


Domain of the equation: 8)x^2)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(20x-(+1/8)x^2)+800=0

We multiply all the terms by the denominator


-(20x-(+1+800*8)x^2)=0


We calculate terms in parentheses: -(20x-(+1+800*8)x^2), so:

20x-(+1+800*8)x^2

We add all the numbers together, and all the variables

20x-6401x^2

We add all the numbers together, and all the variables

-6401x^2+20x

Back to the equation:

-(-6401x^2+20x)


We get rid of parentheses

6401x^2-20x=0

a = 6401; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·6401·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*6401}=\frac{0}{12802}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*6401}=\frac{40}{12802}
=20/6401
$