P-1/p=5p+3p-8

Solution for P-1/p=5p+3p-8 equation:

-1/P=5P+3P-8

We move all terms to the left:

-1/P-(5P+3P-8)=0


Domain of the equation: P!=0

P∈R


We add all the numbers together, and all the variables

-1/P-(8P-8)=0

We get rid of parentheses

-1/P-8P+8=0

We multiply all the terms by the denominator


-8P*P+8*P-1=0

We add all the numbers together, and all the variables

8P-8P*P-1=0

Wy multiply elements

-8P^2+8P-1=0

a = -8; b = 8; c = -1;
Δ = b2-4ac
Δ = 82-4·(-8)·(-1)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{2}}{2*-8}=\frac{-8-4\sqrt{2}}{-16}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{2}}{2*-8}=\frac{-8+4\sqrt{2}}{-16}
$