x=(x-3)(x+7)

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

x=(x-3)(x+7)

We move all terms to the left:

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

We multiply parentheses ..

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

x^2+4x-21

Back to the equation:

-(x^2+4x-21)


We add all the numbers together, and all the variables

x-(x^2+4x-21)=0

We get rid of parentheses

-x^2+x-4x+21=0

We add all the numbers together, and all the variables

-1x^2-3x+21=0

a = -1; b = -3; c = +21;
Δ = b2-4ac
Δ = -32-4·(-1)·21
Δ = 93
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{93}}{2*-1}=\frac{3-\sqrt{93}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{93}}{2*-1}=\frac{3+\sqrt{93}}{-2}
$