30-2p/4p=p

Solution for 30-2p/4p=p equation:

30-2p/4p=p

We move all terms to the left:

30-2p/4p-(p)=0


Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R


We add all the numbers together, and all the variables

-1p-2p/4p+30=0

We multiply all the terms by the denominator


-1p*4p-2p+30*4p=0

We add all the numbers together, and all the variables

-2p-1p*4p+30*4p=0

Wy multiply elements

-4p^2-2p+120p=0

We add all the numbers together, and all the variables

-4p^2+118p=0

a = -4; b = 118; c = 0;
Δ = b2-4ac
Δ = 1182-4·(-4)·0
Δ = 13924
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13924}=118$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(118)-118}{2*-4}=\frac{-236}{-8}
=29+1/2
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(118)+118}{2*-4}=\frac{0}{-8}
=0
$