(x-1)(x-7)=156

Solution for (x-1)(x-7)=156 equation:

(x-1)(x-7)=156

We move all terms to the left:

(x-1)(x-7)-(156)=0

We multiply parentheses ..

(+x^2-7x-1x+7)-156=0

We get rid of parentheses

x^2-7x-1x+7-156=0

We add all the numbers together, and all the variables

x^2-8x-149=0

a = 1; b = -8; c = -149;
Δ = b2-4ac
Δ = -82-4·1·(-149)
Δ = 660
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:

$\sqrt{\Delta}=\sqrt{660}=\sqrt{4*165}=\sqrt{4}*\sqrt{165}=2\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{165}}{2*1}=\frac{8-2\sqrt{165}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{165}}{2*1}=\frac{8+2\sqrt{165}}{2}
$