100=2(8p+5)2p

Solution for 100=2(8p+5)2p equation:

100=2(8p+5)2p

We move all terms to the left:

100-(2(8p+5)2p)=0


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

2(8p+5)2p

We multiply parentheses

32p^2+20p

Back to the equation:

-(32p^2+20p)


We get rid of parentheses

-32p^2-20p+100=0

a = -32; b = -20; c = +100;
Δ = b2-4ac
Δ = -202-4·(-32)·100
Δ = 13200
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:

$\sqrt{\Delta}=\sqrt{13200}=\sqrt{400*33}=\sqrt{400}*\sqrt{33}=20\sqrt{33}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20\sqrt{33}}{2*-32}=\frac{20-20\sqrt{33}}{-64}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20\sqrt{33}}{2*-32}=\frac{20+20\sqrt{33}}{-64}
$