9X(6+j)=81

Solution for 9X(6+j)=81 equation:

9X(6+X)=81

We move all terms to the left:

9X(6+X)-(81)=0

We add all the numbers together, and all the variables

9X(X+6)-81=0

We multiply parentheses

9X^2+54X-81=0

a = 9; b = 54; c = -81;
Δ = b2-4ac
Δ = 542-4·9·(-81)
Δ = 5832
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:

$\sqrt{\Delta}=\sqrt{5832}=\sqrt{2916*2}=\sqrt{2916}*\sqrt{2}=54\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-54\sqrt{2}}{2*9}=\frac{-54-54\sqrt{2}}{18}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+54\sqrt{2}}{2*9}=\frac{-54+54\sqrt{2}}{18}
$