(2x-41)(x+9)=180

Solution for (2x-41)(x+9)=180 equation:

(2x-41)(x+9)=180

We move all terms to the left:

(2x-41)(x+9)-(180)=0

We multiply parentheses ..

(+2x^2+18x-41x-369)-180=0

We get rid of parentheses

2x^2+18x-41x-369-180=0

We add all the numbers together, and all the variables

2x^2-23x-549=0

a = 2; b = -23; c = -549;
Δ = b2-4ac
Δ = -232-4·2·(-549)
Δ = 4921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-\sqrt{4921}}{2*2}=\frac{23-\sqrt{4921}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{4921}}{2*2}=\frac{23+\sqrt{4921}}{4}
$