2x(3x-6)+78=180

Solution for 2x(3x-6)+78=180 equation:

2x(3x-6)+78=180

We move all terms to the left:

2x(3x-6)+78-(180)=0

We add all the numbers together, and all the variables

2x(3x-6)-102=0

We multiply parentheses

6x^2-12x-102=0

a = 6; b = -12; c = -102;
Δ = b2-4ac
Δ = -122-4·6·(-102)
Δ = 2592
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:

$\sqrt{\Delta}=\sqrt{2592}=\sqrt{1296*2}=\sqrt{1296}*\sqrt{2}=36\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-36\sqrt{2}}{2*6}=\frac{12-36\sqrt{2}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+36\sqrt{2}}{2*6}=\frac{12+36\sqrt{2}}{12}
$