10-p=5+1/2p

Solution for 10-p=5+1/2p equation:

10-p=5+1/2p

We move all terms to the left:

10-p-(5+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+5)+10=0

We add all the numbers together, and all the variables

-1p-(1/2p+5)+10=0

We get rid of parentheses

-1p-1/2p-5+10=0

We multiply all the terms by the denominator


-1p*2p-5*2p+10*2p-1=0

Wy multiply elements

-2p^2-10p+20p-1=0

We add all the numbers together, and all the variables

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

a = -2; b = 10; c = -1;
Δ = b2-4ac
Δ = 102-4·(-2)·(-1)
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{23}}{2*-2}=\frac{-10-2\sqrt{23}}{-4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{23}}{2*-2}=\frac{-10+2\sqrt{23}}{-4}
$