p-25=25+1/2p

Solution for p-25=25+1/2p equation:

p-25=25+1/2p

We move all terms to the left:

p-25-(25+1/2p)=0


Domain of the equation: 2p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

p-(1/2p+25)-25=0

We get rid of parentheses

p-1/2p-25-25=0

We multiply all the terms by the denominator


p*2p-25*2p-25*2p-1=0

Wy multiply elements

2p^2-50p-50p-1=0

We add all the numbers together, and all the variables

2p^2-100p-1=0

a = 2; b = -100; c = -1;
Δ = b2-4ac
Δ = -1002-4·2·(-1)
Δ = 10008
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:

$\sqrt{\Delta}=\sqrt{10008}=\sqrt{36*278}=\sqrt{36}*\sqrt{278}=6\sqrt{278}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-6\sqrt{278}}{2*2}=\frac{100-6\sqrt{278}}{4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+6\sqrt{278}}{2*2}=\frac{100+6\sqrt{278}}{4}
$