10-1/2p=-2+1p

Solution for 10-1/2p=-2+1p equation:

10-1/2p=-2+1p

We move all terms to the left:

10-1/2p-(-2+1p)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We add all the numbers together, and all the variables

-1/2p-(p-2)+10=0

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-2p^2+4p+20p-1=0

We add all the numbers together, and all the variables

-2p^2+24p-1=0

a = -2; b = 24; c = -1;
Δ = b2-4ac
Δ = 242-4·(-2)·(-1)
Δ = 568
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:

$\sqrt{\Delta}=\sqrt{568}=\sqrt{4*142}=\sqrt{4}*\sqrt{142}=2\sqrt{142}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{142}}{2*-2}=\frac{-24-2\sqrt{142}}{-4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{142}}{2*-2}=\frac{-24+2\sqrt{142}}{-4}
$