x(x+12)=18^2

Solution for x(x+12)=18^2 equation:

x(x+12)=18^2

We move all terms to the left:

x(x+12)-(18^2)=0

We add all the numbers together, and all the variables

x(x+12)-324=0

We multiply parentheses

x^2+12x-324=0

a = 1; b = 12; c = -324;
Δ = b2-4ac
Δ = 122-4·1·(-324)
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{10}}{2*1}=\frac{-12-12\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{10}}{2*1}=\frac{-12+12\sqrt{10}}{2}
$