p-1/p-12=4/2

Solution for p-1/p-12=4/2 equation:

p-1/p-12=4/2

We move all terms to the left:

p-1/p-12-(4/2)=0


Domain of the equation: p!=0

p∈R


We add all the numbers together, and all the variables

p-1/p-12-2=0

We add all the numbers together, and all the variables

p-1/p-14=0

We multiply all the terms by the denominator


p*p-14*p-1=0

We add all the numbers together, and all the variables

-14p+p*p-1=0

Wy multiply elements

p^2-14p-1=0

a = 1; b = -14; c = -1;
Δ = b2-4ac
Δ = -142-4·1·(-1)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-10\sqrt{2}}{2*1}=\frac{14-10\sqrt{2}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+10\sqrt{2}}{2*1}=\frac{14+10\sqrt{2}}{2}
$