36-7p=-7p(p-5)

Solution for 36-7p=-7p(p-5) equation:

36-7p=-7p(p-5)

We move all terms to the left:

36-7p-(-7p(p-5))=0


We calculate terms in parentheses: -(-7p(p-5)), so:

-7p(p-5)

We multiply parentheses

-7p^2+35p

Back to the equation:

-(-7p^2+35p)


We get rid of parentheses

7p^2-35p-7p+36=0

We add all the numbers together, and all the variables

7p^2-42p+36=0

a = 7; b = -42; c = +36;
Δ = b2-4ac
Δ = -422-4·7·36
Δ = 756
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6\sqrt{21}}{2*7}=\frac{42-6\sqrt{21}}{14}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6\sqrt{21}}{2*7}=\frac{42+6\sqrt{21}}{14}
$