P=-0.5(x-2)(x-12)

Solution for P=-0.5(x-2)(x-12) equation:

=-0.5(P-2)(P-12)

We move all terms to the left:

-(-0.5(P-2)(P-12))=0

We multiply parentheses ..

-(-0.5(+P^2-12P-2P+24))=0


We calculate terms in parentheses: -(-0.5(+P^2-12P-2P+24)), so:

-0.5(+P^2-12P-2P+24)

We multiply parentheses

-0.5P^2+6P+1P-12

We add all the numbers together, and all the variables

-0.5P^2+7P-12

Back to the equation:

-(-0.5P^2+7P-12)


We get rid of parentheses

0.5P^2-7P+12=0

a = 0.5; b = -7; c = +12;
Δ = b2-4ac
Δ = -72-4·0.5·12
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-5}{2*0.5}=\frac{2}{1}
=2
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+5}{2*0.5}=\frac{12}{1}
=12
$