100/2p=45+p

Solution for 100/2p=45+p equation:

100/2p=45+p

We move all terms to the left:

100/2p-(45+p)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We add all the numbers together, and all the variables

100/2p-(p+45)=0

We get rid of parentheses

100/2p-p-45=0

We multiply all the terms by the denominator


-p*2p-45*2p+100=0

Wy multiply elements

-2p^2-90p+100=0

a = -2; b = -90; c = +100;
Δ = b2-4ac
Δ = -902-4·(-2)·100
Δ = 8900
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:

$\sqrt{\Delta}=\sqrt{8900}=\sqrt{100*89}=\sqrt{100}*\sqrt{89}=10\sqrt{89}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-10\sqrt{89}}{2*-2}=\frac{90-10\sqrt{89}}{-4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+10\sqrt{89}}{2*-2}=\frac{90+10\sqrt{89}}{-4}
$