(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^2-10x+21

Back to the equation:

-(x^2-10x+21)


We add all the numbers together, and all the variables

x-(x^2-10x+21)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2+11x-21=0

a = -1; b = 11; c = -21;
Δ = b2-4ac
Δ = 112-4·(-1)·(-21)
Δ = 37
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{-(11)-\sqrt{37}}{2*-1}=\frac{-11-\sqrt{37}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{37}}{2*-1}=\frac{-11+\sqrt{37}}{-2}
$