(x-1)(x+7)=1

Solution for (x-1)(x+7)=1 equation:

(x-1)(x+7)=1

We move all terms to the left:

(x-1)(x+7)-(1)=0

We multiply parentheses ..

(+x^2+7x-1x-7)-1=0

We get rid of parentheses

x^2+7x-1x-7-1=0

We add all the numbers together, and all the variables

x^2+6x-8=0

a = 1; b = 6; c = -8;
Δ = b2-4ac
Δ = 62-4·1·(-8)
Δ = 68
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{17}}{2*1}=\frac{-6-2\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{17}}{2*1}=\frac{-6+2\sqrt{17}}{2}
$