2x(4+6x)=180

Solution for 2x(4+6x)=180 equation:

2x(4+6x)=180

We move all terms to the left:

2x(4+6x)-(180)=0

We add all the numbers together, and all the variables

2x(6x+4)-180=0

We multiply parentheses

12x^2+8x-180=0

a = 12; b = 8; c = -180;
Δ = b2-4ac
Δ = 82-4·12·(-180)
Δ = 8704
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:

$\sqrt{\Delta}=\sqrt{8704}=\sqrt{256*34}=\sqrt{256}*\sqrt{34}=16\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-16\sqrt{34}}{2*12}=\frac{-8-16\sqrt{34}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+16\sqrt{34}}{2*12}=\frac{-8+16\sqrt{34}}{24}
$