18/4.5p=6p+12

Solution for 18/4.5p=6p+12 equation:

18/4.5p=6p+12

We move all terms to the left:

18/4.5p-(6p+12)=0


Domain of the equation: 4.5p!=0

p!=0/4.5

p!=0

p∈R


We get rid of parentheses

18/4.5p-6p-12=0

We multiply all the terms by the denominator


-6p*4.5p-12*4.5p+18=0

Wy multiply elements

-24p^2-48p+18=0

a = -24; b = -48; c = +18;
Δ = b2-4ac
Δ = -482-4·(-24)·18
Δ = 4032
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:

$\sqrt{\Delta}=\sqrt{4032}=\sqrt{576*7}=\sqrt{576}*\sqrt{7}=24\sqrt{7}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-24\sqrt{7}}{2*-24}=\frac{48-24\sqrt{7}}{-48}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+24\sqrt{7}}{2*-24}=\frac{48+24\sqrt{7}}{-48}
$