90/p-2=p-1

Solution for 90/p-2=p-1 equation:

90/p-2=p-1

We move all terms to the left:

90/p-2-(p-1)=0


Domain of the equation: p!=0

p∈R


We get rid of parentheses

90/p-p+1-2=0

We multiply all the terms by the denominator


-p*p+1*p-2*p+90=0

We add all the numbers together, and all the variables

-1p-p*p+90=0

Wy multiply elements

-1p^2-1p+90=0

a = -1; b = -1; c = +90;
Δ = b2-4ac
Δ = -12-4·(-1)·90
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-19}{2*-1}=\frac{-18}{-2}
=+9
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+19}{2*-1}=\frac{20}{-2}
=-10
$