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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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


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

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2+10x-21

Back to the equation:

-(-1x^2+10x-21)


We get rid of parentheses

1x^2-10x+21=0

We add all the numbers together, and all the variables

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