8p-1/p=-7

Solution for 8p-1/p=-7 equation:

8p-1/p=-7

We move all terms to the left:

8p-1/p-(-7)=0


Domain of the equation: p!=0

p∈R


We add all the numbers together, and all the variables

8p-1/p+7=0

We multiply all the terms by the denominator


8p*p+7*p-1=0

We add all the numbers together, and all the variables

7p+8p*p-1=0

Wy multiply elements

8p^2+7p-1=0

a = 8; b = 7; c = -1;
Δ = b2-4ac
Δ = 72-4·8·(-1)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-9}{2*8}=\frac{-16}{16}
=-1
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+9}{2*8}=\frac{2}{16}
=1/8
$