p+10=8/p-7+9

Solution for p+10=8/p-7+9 equation:

p+10=8/p-7+9

We move all terms to the left:

p+10-(8/p-7+9)=0


Domain of the equation: p-7+9)!=0

We move all terms containing p to the left, all other terms to the right

p+9)!=7

p∈R


We add all the numbers together, and all the variables

p-(8/p+2)+10=0

We get rid of parentheses

p-8/p-2+10=0

We multiply all the terms by the denominator


p*p-2*p+10*p-8=0

We add all the numbers together, and all the variables

8p+p*p-8=0

Wy multiply elements

p^2+8p-8=0

a = 1; b = 8; c = -8;
Δ = b2-4ac
Δ = 82-4·1·(-8)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{6}}{2*1}=\frac{-8-4\sqrt{6}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{6}}{2*1}=\frac{-8+4\sqrt{6}}{2}
$