(x-1)(x+1)-9=5x

Solution for (x-1)(x+1)-9=5x equation:

(x-1)(x+1)-9=5x

We move all terms to the left:

(x-1)(x+1)-9-(5x)=0

We add all the numbers together, and all the variables

-5x+(x-1)(x+1)-9=0

We use the square of the difference formula

x^2-5x-1-9=0

We add all the numbers together, and all the variables

x^2-5x-10=0

a = 1; b = -5; c = -10;
Δ = b2-4ac
Δ = -52-4·1·(-10)
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{65}}{2*1}=\frac{5-\sqrt{65}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{65}}{2*1}=\frac{5+\sqrt{65}}{2}
$