(3x-1)(2x+6)=180

Solution for (3x-1)(2x+6)=180 equation:

(3x-1)(2x+6)=180

We move all terms to the left:

(3x-1)(2x+6)-(180)=0

We multiply parentheses ..

(+6x^2+18x-2x-6)-180=0

We get rid of parentheses

6x^2+18x-2x-6-180=0

We add all the numbers together, and all the variables

6x^2+16x-186=0

a = 6; b = 16; c = -186;
Δ = b2-4ac
Δ = 162-4·6·(-186)
Δ = 4720
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:

$\sqrt{\Delta}=\sqrt{4720}=\sqrt{16*295}=\sqrt{16}*\sqrt{295}=4\sqrt{295}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{295}}{2*6}=\frac{-16-4\sqrt{295}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{295}}{2*6}=\frac{-16+4\sqrt{295}}{12}
$