180=9x(9+x)

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

180=9x(9+x)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(9x(x+9)), so:

9x(x+9)

We multiply parentheses

9x^2+81x

Back to the equation:

-(9x^2+81x)


We get rid of parentheses

-9x^2-81x+180=0

a = -9; b = -81; c = +180;
Δ = b2-4ac
Δ = -812-4·(-9)·180
Δ = 13041
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:

$\sqrt{\Delta}=\sqrt{13041}=\sqrt{81*161}=\sqrt{81}*\sqrt{161}=9\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-9\sqrt{161}}{2*-9}=\frac{81-9\sqrt{161}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+9\sqrt{161}}{2*-9}=\frac{81+9\sqrt{161}}{-18}
$