0=(x-7)(x-3)

Solution for 0=(x-7)(x-3) equation:

0=(x-7)(x-3)

We move all terms to the left:

0-((x-7)(x-3))=0

We add all the numbers together, and all the variables

-((x-7)(x-3))=0

We multiply parentheses ..

-((+x^2-3x-7x+21))=0


We calculate terms in parentheses: -((+x^2-3x-7x+21)), so:

(+x^2-3x-7x+21)

We get rid of parentheses

x^2-3x-7x+21

We add all the numbers together, and all the variables

x^2-10x+21

Back to the equation:

-(x^2-10x+21)


We get rid of parentheses

-x^2+10x-21=0

We add all the numbers together, and all the variables

-1x^2+10x-21=0

a = -1; b = 10; c = -21;
Δ = b2-4ac
Δ = 102-4·(-1)·(-21)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4}{2*-1}=\frac{-14}{-2}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4}{2*-1}=\frac{-6}{-2}
=+3
$