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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We multiply parentheses ..

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2+5x-6=0

a = 1; b = 5; c = -6;
Δ = b2-4ac
Δ = 52-4·1·(-6)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-7}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+7}{2*1}=\frac{2}{2}
=1
$