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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

2x^2+2x-1x-1-180=0

We add all the numbers together, and all the variables

2x^2+x-181=0

a = 2; b = 1; c = -181;
Δ = b2-4ac
Δ = 12-4·2·(-181)
Δ = 1449
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:

$\sqrt{\Delta}=\sqrt{1449}=\sqrt{9*161}=\sqrt{9}*\sqrt{161}=3\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{161}}{2*2}=\frac{-1-3\sqrt{161}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{161}}{2*2}=\frac{-1+3\sqrt{161}}{4}
$