x+(3x-6)x+(3x-6)=146

Solution for x+(3x-6)x+(3x-6)=146 equation:

x+(3x-6)x+(3x-6)=146

We move all terms to the left:

x+(3x-6)x+(3x-6)-(146)=0

We multiply parentheses

3x^2+x-6x+(3x-6)-146=0

We get rid of parentheses

3x^2+x-6x+3x-6-146=0

We add all the numbers together, and all the variables

3x^2-2x-152=0

a = 3; b = -2; c = -152;
Δ = b2-4ac
Δ = -22-4·3·(-152)
Δ = 1828
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:

$\sqrt{\Delta}=\sqrt{1828}=\sqrt{4*457}=\sqrt{4}*\sqrt{457}=2\sqrt{457}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{457}}{2*3}=\frac{2-2\sqrt{457}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{457}}{2*3}=\frac{2+2\sqrt{457}}{6}
$