-2/5*p=-6

Solution for -2/5*p=-6 equation:

-2/5*p=-6

We move all terms to the left:

-2/5*p-(-6)=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

-2/5*p+6=0

We multiply all the terms by the denominator


6*5*p-2=0

Wy multiply elements

30p*p-2=0

Wy multiply elements

30p^2-2=0

a = 30; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·30·(-2)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*30}=\frac{0-4\sqrt{15}}{60}
=-\frac{4\sqrt{15}}{60}
=-\frac{\sqrt{15}}{15}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*30}=\frac{0+4\sqrt{15}}{60}
=\frac{4\sqrt{15}}{60}
=\frac{\sqrt{15}}{15}
$