(4x-5)(13x-2)=180

Solution for (4x-5)(13x-2)=180 equation:

(4x-5)(13x-2)=180

We move all terms to the left:

(4x-5)(13x-2)-(180)=0

We multiply parentheses ..

(+52x^2-8x-65x+10)-180=0

We get rid of parentheses

52x^2-8x-65x+10-180=0

We add all the numbers together, and all the variables

52x^2-73x-170=0

a = 52; b = -73; c = -170;
Δ = b2-4ac
Δ = -732-4·52·(-170)
Δ = 40689
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:

$\sqrt{\Delta}=\sqrt{40689}=\sqrt{9*4521}=\sqrt{9}*\sqrt{4521}=3\sqrt{4521}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-73)-3\sqrt{4521}}{2*52}=\frac{73-3\sqrt{4521}}{104}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-73)+3\sqrt{4521}}{2*52}=\frac{73+3\sqrt{4521}}{104}
$