1/4p-3-8p=2

Solution for 1/4p-3-8p=2 equation:

1/4p-3-8p=2

We move all terms to the left:

1/4p-3-8p-(2)=0


Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R


We add all the numbers together, and all the variables

-8p+1/4p-5=0

We multiply all the terms by the denominator


-8p*4p-5*4p+1=0

Wy multiply elements

-32p^2-20p+1=0

a = -32; b = -20; c = +1;
Δ = b2-4ac
Δ = -202-4·(-32)·1
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{33}}{2*-32}=\frac{20-4\sqrt{33}}{-64}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{33}}{2*-32}=\frac{20+4\sqrt{33}}{-64}
$