2p+p=1/4*2p+150

Solution for 2p+p=1/4*2p+150 equation:

2p+p=1/4*2p+150

We move all terms to the left:

2p+p-(1/4*2p+150)=0


Domain of the equation: 4*2p+150)!=0

p∈R


We add all the numbers together, and all the variables

3p-(1/4*2p+150)=0

We get rid of parentheses

3p-1/4*2p-150=0

We multiply all the terms by the denominator


3p*4*2p-150*4*2p-1=0

Wy multiply elements

24p^2*2-1200p*2-1=0

Wy multiply elements

48p^2-2400p-1=0

a = 48; b = -2400; c = -1;
Δ = b2-4ac
Δ = -24002-4·48·(-1)
Δ = 5760192
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:

$\sqrt{\Delta}=\sqrt{5760192}=\sqrt{64*90003}=\sqrt{64}*\sqrt{90003}=8\sqrt{90003}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2400)-8\sqrt{90003}}{2*48}=\frac{2400-8\sqrt{90003}}{96}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2400)+8\sqrt{90003}}{2*48}=\frac{2400+8\sqrt{90003}}{96}
$