4/3p-3=8p+12

Solution for 4/3p-3=8p+12 equation:

4/3p-3=8p+12

We move all terms to the left:

4/3p-3-(8p+12)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R


We get rid of parentheses

4/3p-8p-12-3=0

We multiply all the terms by the denominator


-8p*3p-12*3p-3*3p+4=0

Wy multiply elements

-24p^2-36p-9p+4=0

We add all the numbers together, and all the variables

-24p^2-45p+4=0

a = -24; b = -45; c = +4;
Δ = b2-4ac
Δ = -452-4·(-24)·4
Δ = 2409
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{-(-45)-\sqrt{2409}}{2*-24}=\frac{45-\sqrt{2409}}{-48}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2409}}{2*-24}=\frac{45+\sqrt{2409}}{-48}
$