6x=(-x+12)(-x+12)

Solution for 6x=(-x+12)(-x+12) equation:

6x=(-x+12)(-x+12)

We move all terms to the left:

6x-((-x+12)(-x+12))=0

We add all the numbers together, and all the variables

6x-((-1x+12)(-1x+12))=0

We multiply parentheses ..

-((+x^2-12x-12x+144))+6x=0


We calculate terms in parentheses: -((+x^2-12x-12x+144)), so:

(+x^2-12x-12x+144)

We get rid of parentheses

x^2-12x-12x+144

We add all the numbers together, and all the variables

x^2-24x+144

Back to the equation:

-(x^2-24x+144)


We add all the numbers together, and all the variables

6x-(x^2-24x+144)=0

We get rid of parentheses

-x^2+6x+24x-144=0

We add all the numbers together, and all the variables

-1x^2+30x-144=0

a = -1; b = 30; c = -144;
Δ = b2-4ac
Δ = 302-4·(-1)·(-144)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-18}{2*-1}=\frac{-48}{-2}
=+24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+18}{2*-1}=\frac{-12}{-2}
=+6
$