93=5-2(p-8)4p

Solution for 93=5-2(p-8)4p equation:

93=5-2(p-8)4p

We move all terms to the left:

93-(5-2(p-8)4p)=0


We calculate terms in parentheses: -(5-2(p-8)4p), so:

5-2(p-8)4p

determiningTheFunctionDomain
-2(p-8)4p+5

We multiply parentheses

-8p^2+64p+5

Back to the equation:

-(-8p^2+64p+5)


We get rid of parentheses

8p^2-64p-5+93=0

We add all the numbers together, and all the variables

8p^2-64p+88=0

a = 8; b = -64; c = +88;
Δ = b2-4ac
Δ = -642-4·8·88
Δ = 1280
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:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-16\sqrt{5}}{2*8}=\frac{64-16\sqrt{5}}{16}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+16\sqrt{5}}{2*8}=\frac{64+16\sqrt{5}}{16}
$