2x(x+9)+60=180

Solution for 2x(x+9)+60=180 equation:

2x(x+9)+60=180

We move all terms to the left:

2x(x+9)+60-(180)=0

We add all the numbers together, and all the variables

2x(x+9)-120=0

We multiply parentheses

2x^2+18x-120=0

a = 2; b = 18; c = -120;
Δ = b2-4ac
Δ = 182-4·2·(-120)
Δ = 1284
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:

$\sqrt{\Delta}=\sqrt{1284}=\sqrt{4*321}=\sqrt{4}*\sqrt{321}=2\sqrt{321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{321}}{2*2}=\frac{-18-2\sqrt{321}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{321}}{2*2}=\frac{-18+2\sqrt{321}}{4}
$