9x(9+x)=27

Solution for 9x(9+x)=27 equation:

9x(9+x)=27

We move all terms to the left:

9x(9+x)-(27)=0

We add all the numbers together, and all the variables

9x(x+9)-27=0

We multiply parentheses

9x^2+81x-27=0

a = 9; b = 81; c = -27;
Δ = b2-4ac
Δ = 812-4·9·(-27)
Δ = 7533
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:

$\sqrt{\Delta}=\sqrt{7533}=\sqrt{81*93}=\sqrt{81}*\sqrt{93}=9\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(81)-9\sqrt{93}}{2*9}=\frac{-81-9\sqrt{93}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+9\sqrt{93}}{2*9}=\frac{-81+9\sqrt{93}}{18}
$