(1/3)p-3=144

Solution for (1/3)p-3=144 equation:

(1/3)p-3=144

We move all terms to the left:

(1/3)p-3-(144)=0


Domain of the equation: 3)p!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

(+1/3)p-3-144=0

We add all the numbers together, and all the variables

(+1/3)p-147=0

We multiply parentheses

p^2-147=0

a = 1; b = 0; c = -147;
Δ = b2-4ac
Δ = 02-4·1·(-147)
Δ = 588
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:

$\sqrt{\Delta}=\sqrt{588}=\sqrt{196*3}=\sqrt{196}*\sqrt{3}=14\sqrt{3}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{3}}{2*1}=\frac{0-14\sqrt{3}}{2}
=-\frac{14\sqrt{3}}{2}
=-7\sqrt{3}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{3}}{2*1}=\frac{0+14\sqrt{3}}{2}
=\frac{14\sqrt{3}}{2}
=7\sqrt{3}
$