-4+8p-6p-5/20p=

Solution for -4+8p-6p-5/20p= equation:

-4+8p-6p-5/20p=

We move all terms to the left:

-4+8p-6p-5/20p-()=0


Domain of the equation: 20p!=0

p!=0/20

p!=0

p∈R


We add all the numbers together, and all the variables

2p-5/20p=0

We multiply all the terms by the denominator


2p*20p-5=0

Wy multiply elements

40p^2-5=0

a = 40; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·40·(-5)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{2}}{2*40}=\frac{0-20\sqrt{2}}{80}
=-\frac{20\sqrt{2}}{80}
=-\frac{\sqrt{2}}{4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{2}}{2*40}=\frac{0+20\sqrt{2}}{80}
=\frac{20\sqrt{2}}{80}
=\frac{\sqrt{2}}{4}
$