x=(x-4)(x+6)

Solution for x=(x-4)(x+6) equation:

x=(x-4)(x+6)

We move all terms to the left:

x-((x-4)(x+6))=0

We multiply parentheses ..

-((+x^2+6x-4x-24))+x=0


We calculate terms in parentheses: -((+x^2+6x-4x-24)), so:

(+x^2+6x-4x-24)

We get rid of parentheses

x^2+6x-4x-24

We add all the numbers together, and all the variables

x^2+2x-24

Back to the equation:

-(x^2+2x-24)


We add all the numbers together, and all the variables

x-(x^2+2x-24)=0

We get rid of parentheses

-x^2+x-2x+24=0

We add all the numbers together, and all the variables

-1x^2-1x+24=0

a = -1; b = -1; c = +24;
Δ = b2-4ac
Δ = -12-4·(-1)·24
Δ = 97
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{-(-1)-\sqrt{97}}{2*-1}=\frac{1-\sqrt{97}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{97}}{2*-1}=\frac{1+\sqrt{97}}{-2}
$