(9/8*p)=27

Solution for (9/8*p)=27 equation:

(9/8*p)=27

We move all terms to the left:

(9/8*p)-(27)=0


Domain of the equation: 8*p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

(+9/8*p)-27=0

We get rid of parentheses

9/8*p-27=0

We multiply all the terms by the denominator


-27*8*p+9=0

Wy multiply elements

-216p*p+9=0

Wy multiply elements

-216p^2+9=0

a = -216; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-216)·9
Δ = 7776
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:

$\sqrt{\Delta}=\sqrt{7776}=\sqrt{1296*6}=\sqrt{1296}*\sqrt{6}=36\sqrt{6}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{6}}{2*-216}=\frac{0-36\sqrt{6}}{-432}
=-\frac{36\sqrt{6}}{-432}
=-\frac{\sqrt{6}}{-12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{6}}{2*-216}=\frac{0+36\sqrt{6}}{-432}
=\frac{36\sqrt{6}}{-432}
=\frac{\sqrt{6}}{-12}
$