X(19x+80)=180

Solution for X(19x+80)=180 equation:

X(19X+80)=180

We move all terms to the left:

X(19X+80)-(180)=0

We multiply parentheses

19X^2+80X-180=0

a = 19; b = 80; c = -180;
Δ = b2-4ac
Δ = 802-4·19·(-180)
Δ = 20080
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:

$\sqrt{\Delta}=\sqrt{20080}=\sqrt{16*1255}=\sqrt{16}*\sqrt{1255}=4\sqrt{1255}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-4\sqrt{1255}}{2*19}=\frac{-80-4\sqrt{1255}}{38}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+4\sqrt{1255}}{2*19}=\frac{-80+4\sqrt{1255}}{38}
$