9x(X+1)=54/6

Solution for 9x(X+1)=54/6 equation:

9x(x+1)=54/6

We move all terms to the left:

9x(x+1)-(54/6)=0

We add all the numbers together, and all the variables

9x(x+1)-9=0

We multiply parentheses

9x^2+9x-9=0

a = 9; b = 9; c = -9;
Δ = b2-4ac
Δ = 92-4·9·(-9)
Δ = 405
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:

$\sqrt{\Delta}=\sqrt{405}=\sqrt{81*5}=\sqrt{81}*\sqrt{5}=9\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9\sqrt{5}}{2*9}=\frac{-9-9\sqrt{5}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9\sqrt{5}}{2*9}=\frac{-9+9\sqrt{5}}{18}
$