p=7/p+10

Solution for p=7/p+10 equation:

p=7/p+10

We move all terms to the left:

p-(7/p+10)=0


Domain of the equation: p+10)!=0

p∈R


We get rid of parentheses

p-7/p-10=0

We multiply all the terms by the denominator


p*p-10*p-7=0

We add all the numbers together, and all the variables

-10p+p*p-7=0

Wy multiply elements

p^2-10p-7=0

a = 1; b = -10; c = -7;
Δ = b2-4ac
Δ = -102-4·1·(-7)
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-8\sqrt{2}}{2*1}=\frac{10-8\sqrt{2}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+8\sqrt{2}}{2*1}=\frac{10+8\sqrt{2}}{2}
$