1728=x(x+12)

Solution for 1728=x(x+12) equation:

1728=x(x+12)

We move all terms to the left:

1728-(x(x+12))=0


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

x(x+12)

We multiply parentheses

x^2+12x

Back to the equation:

-(x^2+12x)


We get rid of parentheses

-x^2-12x+1728=0

We add all the numbers together, and all the variables

-1x^2-12x+1728=0

a = -1; b = -12; c = +1728;
Δ = b2-4ac
Δ = -122-4·(-1)·1728
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-84}{2*-1}=\frac{-72}{-2}
=+36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+84}{2*-1}=\frac{96}{-2}
=-48
$