L(x)=400*(20-x)*(x-4)

Solution for L(x)=400*(20-x)*(x-4) equation:

(L)=400(20-L)(L-4)

We move all terms to the left:

(L)-(400(20-L)(L-4))=0

We add all the numbers together, and all the variables

L-(400(-1L+20)(L-4))=0

We multiply parentheses ..

-(400(-1L^2+4L+20L-80))+L=0


We calculate terms in parentheses: -(400(-1L^2+4L+20L-80)), so:

400(-1L^2+4L+20L-80)

We multiply parentheses

-400L^2+1600L+8000L-32000

We add all the numbers together, and all the variables

-400L^2+9600L-32000

Back to the equation:

-(-400L^2+9600L-32000)


We get rid of parentheses

400L^2-9600L+L+32000=0

We add all the numbers together, and all the variables

400L^2-9599L+32000=0

a = 400; b = -9599; c = +32000;
Δ = b2-4ac
Δ = -95992-4·400·32000
Δ = 40940801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$L_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$L_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$L_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9599)-\sqrt{40940801}}{2*400}=\frac{9599-\sqrt{40940801}}{800}
$
$L_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9599)+\sqrt{40940801}}{2*400}=\frac{9599+\sqrt{40940801}}{800}
$