18x(-2x-4)+12=-52

Solution for 18x(-2x-4)+12=-52 equation:

18x(-2x-4)+12=-52

We move all terms to the left:

18x(-2x-4)+12-(-52)=0

We add all the numbers together, and all the variables

18x(-2x-4)+64=0

We multiply parentheses

-36x^2-72x+64=0

a = -36; b = -72; c = +64;
Δ = b2-4ac
Δ = -722-4·(-36)·64
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-120}{2*-36}=\frac{-48}{-72}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+120}{2*-36}=\frac{192}{-72}
=-2+2/3
$