x^2+12x=1728

Solution for x^2+12x=1728 equation:

x^2+12x=1728

We move all terms to the left:

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