(4x-13)(2x-13)(5+19)=180

Solution for (4x-13)(2x-13)(5+19)=180 equation:

(4x-13)(2x-13)(5+19)=180

We move all terms to the left:

(4x-13)(2x-13)(5+19)-(180)=0

We add all the numbers together, and all the variables

(4x-13)(2x-13)24-180=0

We multiply parentheses ..

(+8x^2-52x-26x+169)24-180=0

We multiply parentheses

192x^2-1248x-624x+4056-180=0

We add all the numbers together, and all the variables

192x^2-1872x+3876=0

a = 192; b = -1872; c = +3876;
Δ = b2-4ac
Δ = -18722-4·192·3876
Δ = 527616
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:

$\sqrt{\Delta}=\sqrt{527616}=\sqrt{2304*229}=\sqrt{2304}*\sqrt{229}=48\sqrt{229}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1872)-48\sqrt{229}}{2*192}=\frac{1872-48\sqrt{229}}{384}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1872)+48\sqrt{229}}{2*192}=\frac{1872+48\sqrt{229}}{384}
$