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

Solution for (x=7)(x-2)(x+3) equation:

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

We move all terms to the left:

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

We multiply parentheses ..

(x-7(+x^2+3x-2x-6))=0


We calculate terms in parentheses: +(x-7(+x^2+3x-2x-6)), so:

x-7(+x^2+3x-2x-6)

determiningTheFunctionDomain
-7(+x^2+3x-2x-6)+x

We multiply parentheses

-7x^2-21x+14x+x+42

We add all the numbers together, and all the variables

-7x^2-6x+42

Back to the equation:

+(-7x^2-6x+42)


We get rid of parentheses

-7x^2-6x+42=0

a = -7; b = -6; c = +42;
Δ = b2-4ac
Δ = -62-4·(-7)·42
Δ = 1212
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1212}=\sqrt{4*303}=\sqrt{4}*\sqrt{303}=2\sqrt{303}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{303}}{2*-7}=\frac{6-2\sqrt{303}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{303}}{2*-7}=\frac{6+2\sqrt{303}}{-14}
$