(-1/5)p+(9/5)p+6=30

Solution for (-1/5)p+(9/5)p+6=30 equation:

(-1/5)p+(9/5)p+6=30

We move all terms to the left:

(-1/5)p+(9/5)p+6-(30)=0


Domain of the equation: 5)p!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

(-1/5)p+(+9/5)p+6-30=0

We add all the numbers together, and all the variables

(-1/5)p+(+9/5)p-24=0

We multiply parentheses

-1p^2+9p^2-24=0

We add all the numbers together, and all the variables

8p^2-24=0

a = 8; b = 0; c = -24;
Δ = b2-4ac
Δ = 02-4·8·(-24)
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{3}}{2*8}=\frac{0-16\sqrt{3}}{16}
=-\frac{16\sqrt{3}}{16}
=-\sqrt{3}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{3}}{2*8}=\frac{0+16\sqrt{3}}{16}
=\frac{16\sqrt{3}}{16}
=\sqrt{3}
$