(2x-1)(3x-19)=180

Solution for (2x-1)(3x-19)=180 equation:

(2x-1)(3x-19)=180

We move all terms to the left:

(2x-1)(3x-19)-(180)=0

We multiply parentheses ..

(+6x^2-38x-3x+19)-180=0

We get rid of parentheses

6x^2-38x-3x+19-180=0

We add all the numbers together, and all the variables

6x^2-41x-161=0

a = 6; b = -41; c = -161;
Δ = b2-4ac
Δ = -412-4·6·(-161)
Δ = 5545
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{-(-41)-\sqrt{5545}}{2*6}=\frac{41-\sqrt{5545}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+\sqrt{5545}}{2*6}=\frac{41+\sqrt{5545}}{12}
$