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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-4x-186=0

a = 2; b = -4; c = -186;
Δ = b2-4ac
Δ = -42-4·2·(-186)
Δ = 1504
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:

$\sqrt{\Delta}=\sqrt{1504}=\sqrt{16*94}=\sqrt{16}*\sqrt{94}=4\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{94}}{2*2}=\frac{4-4\sqrt{94}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{94}}{2*2}=\frac{4+4\sqrt{94}}{4}
$