x(x+12)=12(12)

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

x(x+12)=12(12)

We move all terms to the left:

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

determiningTheFunctionDomain
x(x+12)-1212=0

We multiply parentheses

x^2+12x-1212=0

a = 1; b = 12; c = -1212;
Δ = b2-4ac
Δ = 122-4·1·(-1212)
Δ = 4992
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:

$\sqrt{\Delta}=\sqrt{4992}=\sqrt{64*78}=\sqrt{64}*\sqrt{78}=8\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8\sqrt{78}}{2*1}=\frac{-12-8\sqrt{78}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8\sqrt{78}}{2*1}=\frac{-12+8\sqrt{78}}{2}
$