L(x)=-x2+6x

Solution for L(x)=-x2+6x equation:

(L)=-L2+6L

We move all terms to the left:

(L)-(-L2+6L)=0

We add all the numbers together, and all the variables

-(-1L^2+6L)+L=0

We get rid of parentheses

1L^2-6L+L=0

We add all the numbers together, and all the variables

L^2-5L=0

a = 1; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·1·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$L_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$L_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$L_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*1}=\frac{0}{2}
=0
$
$L_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*1}=\frac{10}{2}
=5
$