12-p(p=7)

Solution for 12-p(p=7) equation:

12-p(p=7)

We move all terms to the left:

12-p(p-(7))=0

We multiply parentheses

-p^2+7p+12=0

We add all the numbers together, and all the variables

-1p^2+7p+12=0

a = -1; b = 7; c = +12;
Δ = b2-4ac
Δ = 72-4·(-1)·12
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{97}}{2*-1}=\frac{-7-\sqrt{97}}{-2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{97}}{2*-1}=\frac{-7+\sqrt{97}}{-2}
$