L(p)=(p+8)(8-p)

Solution for L(p)=(p+8)(8-p) equation:

(L)=(L+8)(8-L)

We move all terms to the left:

(L)-((L+8)(8-L))=0

We add all the numbers together, and all the variables

L-((L+8)(-1L+8))=0

We multiply parentheses ..

-((-1L^2+8L-8L+64))+L=0


We calculate terms in parentheses: -((-1L^2+8L-8L+64)), so:

(-1L^2+8L-8L+64)

We get rid of parentheses

-1L^2+8L-8L+64

We add all the numbers together, and all the variables

-1L^2+64

Back to the equation:

-(-1L^2+64)


We get rid of parentheses

1L^2+L-64=0

We add all the numbers together, and all the variables

L^2+L-64=0

a = 1; b = 1; c = -64;
Δ = b2-4ac
Δ = 12-4·1·(-64)
Δ = 257
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{-(1)-\sqrt{257}}{2*1}=\frac{-1-\sqrt{257}}{2}
$
$L_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{257}}{2*1}=\frac{-1+\sqrt{257}}{2}
$