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

Solution for (x+1)(x-7)=(x-1)2 equation:

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

We move all terms to the left:

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((x-1)2), so:

(x-1)2

We multiply parentheses

2x-2

Back to the equation:

-(2x-2)


We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-8x-5=0

a = 1; b = -8; c = -5;
Δ = b2-4ac
Δ = -82-4·1·(-5)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{21}}{2*1}=\frac{8-2\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{21}}{2*1}=\frac{8+2\sqrt{21}}{2}
$