p-16=-4/9p+1

Solution for p-16=-4/9p+1 equation:

p-16=-4/9p+1

We move all terms to the left:

p-16-(-4/9p+1)=0


Domain of the equation: 9p+1)!=0

p∈R


We get rid of parentheses

p+4/9p-1-16=0

We multiply all the terms by the denominator


p*9p-1*9p-16*9p+4=0

Wy multiply elements

9p^2-9p-144p+4=0

We add all the numbers together, and all the variables

9p^2-153p+4=0

a = 9; b = -153; c = +4;
Δ = b2-4ac
Δ = -1532-4·9·4
Δ = 23265
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:

$\sqrt{\Delta}=\sqrt{23265}=\sqrt{9*2585}=\sqrt{9}*\sqrt{2585}=3\sqrt{2585}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-153)-3\sqrt{2585}}{2*9}=\frac{153-3\sqrt{2585}}{18}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-153)+3\sqrt{2585}}{2*9}=\frac{153+3\sqrt{2585}}{18}
$