p-9=1/4p+3

Solution for p-9=1/4p+3 equation:

p-9=1/4p+3

We move all terms to the left:

p-9-(1/4p+3)=0


Domain of the equation: 4p+3)!=0

p∈R


We get rid of parentheses

p-1/4p-3-9=0

We multiply all the terms by the denominator


p*4p-3*4p-9*4p-1=0

Wy multiply elements

4p^2-12p-36p-1=0

We add all the numbers together, and all the variables

4p^2-48p-1=0

a = 4; b = -48; c = -1;
Δ = b2-4ac
Δ = -482-4·4·(-1)
Δ = 2320
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:

$\sqrt{\Delta}=\sqrt{2320}=\sqrt{16*145}=\sqrt{16}*\sqrt{145}=4\sqrt{145}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{145}}{2*4}=\frac{48-4\sqrt{145}}{8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{145}}{2*4}=\frac{48+4\sqrt{145}}{8}
$