5-1/2p=p-1

Solution for 5-1/2p=p-1 equation:

5-1/2p=p-1

We move all terms to the left:

5-1/2p-(p-1)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We get rid of parentheses

-1/2p-p+1+5=0

We multiply all the terms by the denominator


-p*2p+1*2p+5*2p-1=0

Wy multiply elements

-2p^2+2p+10p-1=0

We add all the numbers together, and all the variables

-2p^2+12p-1=0

a = -2; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·(-2)·(-1)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{34}}{2*-2}=\frac{-12-2\sqrt{34}}{-4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{34}}{2*-2}=\frac{-12+2\sqrt{34}}{-4}
$