6x(x+19)=180

Solution for 6x(x+19)=180 equation:

6x(x+19)=180

We move all terms to the left:

6x(x+19)-(180)=0

We multiply parentheses

6x^2+114x-180=0

a = 6; b = 114; c = -180;
Δ = b2-4ac
Δ = 1142-4·6·(-180)
Δ = 17316
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:

$\sqrt{\Delta}=\sqrt{17316}=\sqrt{36*481}=\sqrt{36}*\sqrt{481}=6\sqrt{481}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(114)-6\sqrt{481}}{2*6}=\frac{-114-6\sqrt{481}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(114)+6\sqrt{481}}{2*6}=\frac{-114+6\sqrt{481}}{12}
$