3/2p=15p=

Solution for 3/2p=15p= equation:

3/2p=15p=

We move all terms to the left:

3/2p-(15p)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We add all the numbers together, and all the variables

-15p+3/2p=0

We multiply all the terms by the denominator


-15p*2p+3=0

Wy multiply elements

-30p^2+3=0

a = -30; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-30)·3
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{10}}{2*-30}=\frac{0-6\sqrt{10}}{-60}
=-\frac{6\sqrt{10}}{-60}
=-\frac{\sqrt{10}}{-10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{10}}{2*-30}=\frac{0+6\sqrt{10}}{-60}
=\frac{6\sqrt{10}}{-60}
=\frac{\sqrt{10}}{-10}
$