4/3p+5=4p+2

Solution for 4/3p+5=4p+2 equation:

4/3p+5=4p+2

We move all terms to the left:

4/3p+5-(4p+2)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R


We get rid of parentheses

4/3p-4p-2+5=0

We multiply all the terms by the denominator


-4p*3p-2*3p+5*3p+4=0

Wy multiply elements

-12p^2-6p+15p+4=0

We add all the numbers together, and all the variables

-12p^2+9p+4=0

a = -12; b = 9; c = +4;
Δ = b2-4ac
Δ = 92-4·(-12)·4
Δ = 273
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{-(9)-\sqrt{273}}{2*-12}=\frac{-9-\sqrt{273}}{-24}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{273}}{2*-12}=\frac{-9+\sqrt{273}}{-24}
$