(20x-5)19x=180

Solution for (20x-5)19x=180 equation:

(20x-5)19x=180

We move all terms to the left:

(20x-5)19x-(180)=0

We multiply parentheses

380x^2-95x-180=0

a = 380; b = -95; c = -180;
Δ = b2-4ac
Δ = -952-4·380·(-180)
Δ = 282625
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:

$\sqrt{\Delta}=\sqrt{282625}=\sqrt{25*11305}=\sqrt{25}*\sqrt{11305}=5\sqrt{11305}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-95)-5\sqrt{11305}}{2*380}=\frac{95-5\sqrt{11305}}{760}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-95)+5\sqrt{11305}}{2*380}=\frac{95+5\sqrt{11305}}{760}
$