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

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

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

We move all terms to the left:

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


Domain of the equation: 3p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-1p*3p+3*3p+144*3p-1=0

Wy multiply elements

-3p^2+9p+432p-1=0

We add all the numbers together, and all the variables

-3p^2+441p-1=0

a = -3; b = 441; c = -1;
Δ = b2-4ac
Δ = 4412-4·(-3)·(-1)
Δ = 194469
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{-(441)-\sqrt{194469}}{2*-3}=\frac{-441-\sqrt{194469}}{-6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(441)+\sqrt{194469}}{2*-3}=\frac{-441+\sqrt{194469}}{-6}
$