7(x-7)(x-8)=x-7

Solution for 7(x-7)(x-8)=x-7 equation:

7(x-7)(x-8)=x-7

We move all terms to the left:

7(x-7)(x-8)-(x-7)=0

We get rid of parentheses

7(x-7)(x-8)-x+7=0

We multiply parentheses ..

7(+x^2-8x-7x+56)-x+7=0

We add all the numbers together, and all the variables

7(+x^2-8x-7x+56)-1x+7=0

We multiply parentheses

7x^2-56x-49x-1x+392+7=0

We add all the numbers together, and all the variables

7x^2-106x+399=0

a = 7; b = -106; c = +399;
Δ = b2-4ac
Δ = -1062-4·7·399
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-106)-8}{2*7}=\frac{98}{14}
=7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-106)+8}{2*7}=\frac{114}{14}
=8+1/7
$