14-p=1/3p-1

Solution for 14-p=1/3p-1 equation:

14-p=1/3p-1

We move all terms to the left:

14-p-(1/3p-1)=0


Domain of the equation: 3p-1)!=0

p∈R


We add all the numbers together, and all the variables

-1p-(1/3p-1)+14=0

We get rid of parentheses

-1p-1/3p+1+14=0

We multiply all the terms by the denominator


-1p*3p+1*3p+14*3p-1=0

Wy multiply elements

-3p^2+3p+42p-1=0

We add all the numbers together, and all the variables

-3p^2+45p-1=0

a = -3; b = 45; c = -1;
Δ = b2-4ac
Δ = 452-4·(-3)·(-1)
Δ = 2013
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-\sqrt{2013}}{2*-3}=\frac{-45-\sqrt{2013}}{-6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2013}}{2*-3}=\frac{-45+\sqrt{2013}}{-6}
$