x(x+30)+2x=180

Solution for x(x+30)+2x=180 equation:

x(x+30)+2x=180

We move all terms to the left:

x(x+30)+2x-(180)=0

We add all the numbers together, and all the variables

2x+x(x+30)-180=0

We multiply parentheses

x^2+2x+30x-180=0

We add all the numbers together, and all the variables

x^2+32x-180=0

a = 1; b = 32; c = -180;
Δ = b2-4ac
Δ = 322-4·1·(-180)
Δ = 1744
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:

$\sqrt{\Delta}=\sqrt{1744}=\sqrt{16*109}=\sqrt{16}*\sqrt{109}=4\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{109}}{2*1}=\frac{-32-4\sqrt{109}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{109}}{2*1}=\frac{-32+4\sqrt{109}}{2}
$