6p+2=26/p

Solution for 6p+2=26/p equation:

6p+2=26/p

We move all terms to the left:

6p+2-(26/p)=0


Domain of the equation: p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

6p-(+26/p)+2=0

We get rid of parentheses

6p-26/p+2=0

We multiply all the terms by the denominator


6p*p+2*p-26=0

We add all the numbers together, and all the variables

2p+6p*p-26=0

Wy multiply elements

6p^2+2p-26=0

a = 6; b = 2; c = -26;
Δ = b2-4ac
Δ = 22-4·6·(-26)
Δ = 628
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:

$\sqrt{\Delta}=\sqrt{628}=\sqrt{4*157}=\sqrt{4}*\sqrt{157}=2\sqrt{157}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{157}}{2*6}=\frac{-2-2\sqrt{157}}{12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{157}}{2*6}=\frac{-2+2\sqrt{157}}{12}
$