(x(x-9))=1

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

(x(x-9))=1

We move all terms to the left:

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


We calculate terms in parentheses: +(x(x-9)), so:

x(x-9)

We multiply parentheses

x^2-9x

Back to the equation:

+(x^2-9x)


We get rid of parentheses

x^2-9x-1=0

a = 1; b = -9; c = -1;
Δ = b2-4ac
Δ = -92-4·1·(-1)
Δ = 85
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{-(-9)-\sqrt{85}}{2*1}=\frac{9-\sqrt{85}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{85}}{2*1}=\frac{9+\sqrt{85}}{2}
$