(x-6)(x-3)=-1

Solution for (x-6)(x-3)=-1 equation:

(x-6)(x-3)=-1

We move all terms to the left:

(x-6)(x-3)-(-1)=0

We add all the numbers together, and all the variables

(x-6)(x-3)+1=0

We multiply parentheses ..

(+x^2-3x-6x+18)+1=0

We get rid of parentheses

x^2-3x-6x+18+1=0

We add all the numbers together, and all the variables

x^2-9x+19=0

a = 1; b = -9; c = +19;
Δ = b2-4ac
Δ = -92-4·1·19
Δ = 5
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{5}}{2*1}=\frac{9-\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{5}}{2*1}=\frac{9+\sqrt{5}}{2}
$