40=(x-7)(x-1)

Solution for 40=(x-7)(x-1) equation:

40=(x-7)(x-1)

We move all terms to the left:

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

We multiply parentheses ..

-((+x^2-1x-7x+7))+40=0


We calculate terms in parentheses: -((+x^2-1x-7x+7)), so:

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

We get rid of parentheses

x^2-1x-7x+7

We add all the numbers together, and all the variables

x^2-8x+7

Back to the equation:

-(x^2-8x+7)


We get rid of parentheses

-x^2+8x-7+40=0

We add all the numbers together, and all the variables

-1x^2+8x+33=0

a = -1; b = 8; c = +33;
Δ = b2-4ac
Δ = 82-4·(-1)·33
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-14}{2*-1}=\frac{-22}{-2}
=+11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+14}{2*-1}=\frac{6}{-2}
=-3
$