(7x-1)(13x-19)=180

Solution for (7x-1)(13x-19)=180 equation:

(7x-1)(13x-19)=180

We move all terms to the left:

(7x-1)(13x-19)-(180)=0

We multiply parentheses ..

(+91x^2-133x-13x+19)-180=0

We get rid of parentheses

91x^2-133x-13x+19-180=0

We add all the numbers together, and all the variables

91x^2-146x-161=0

a = 91; b = -146; c = -161;
Δ = b2-4ac
Δ = -1462-4·91·(-161)
Δ = 79920
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:

$\sqrt{\Delta}=\sqrt{79920}=\sqrt{144*555}=\sqrt{144}*\sqrt{555}=12\sqrt{555}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-146)-12\sqrt{555}}{2*91}=\frac{146-12\sqrt{555}}{182}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-146)+12\sqrt{555}}{2*91}=\frac{146+12\sqrt{555}}{182}
$