30-1/3p=p+14

Solution for 30-1/3p=p+14 equation:

30-1/3p=p+14

We move all terms to the left:

30-1/3p-(p+14)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R


We get rid of parentheses

-1/3p-p-14+30=0

We multiply all the terms by the denominator


-p*3p-14*3p+30*3p-1=0

Wy multiply elements

-3p^2-42p+90p-1=0

We add all the numbers together, and all the variables

-3p^2+48p-1=0

a = -3; b = 48; c = -1;
Δ = b2-4ac
Δ = 482-4·(-3)·(-1)
Δ = 2292
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:

$\sqrt{\Delta}=\sqrt{2292}=\sqrt{4*573}=\sqrt{4}*\sqrt{573}=2\sqrt{573}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-2\sqrt{573}}{2*-3}=\frac{-48-2\sqrt{573}}{-6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+2\sqrt{573}}{2*-3}=\frac{-48+2\sqrt{573}}{-6}
$