30+9x(30+x)=180

Solution for 30+9x(30+x)=180 equation:

30+9x(30+x)=180

We move all terms to the left:

30+9x(30+x)-(180)=0

We add all the numbers together, and all the variables

9x(x+30)+30-180=0

We add all the numbers together, and all the variables

9x(x+30)-150=0

We multiply parentheses

9x^2+270x-150=0

a = 9; b = 270; c = -150;
Δ = b2-4ac
Δ = 2702-4·9·(-150)
Δ = 78300
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:

$\sqrt{\Delta}=\sqrt{78300}=\sqrt{900*87}=\sqrt{900}*\sqrt{87}=30\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(270)-30\sqrt{87}}{2*9}=\frac{-270-30\sqrt{87}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(270)+30\sqrt{87}}{2*9}=\frac{-270+30\sqrt{87}}{18}
$