9x(3x-9)=6+5x

Solution for 9x(3x-9)=6+5x equation:

9x(3x-9)=6+5x

We move all terms to the left:

9x(3x-9)-(6+5x)=0

We add all the numbers together, and all the variables

9x(3x-9)-(5x+6)=0

We multiply parentheses

27x^2-81x-(5x+6)=0

We get rid of parentheses

27x^2-81x-5x-6=0

We add all the numbers together, and all the variables

27x^2-86x-6=0

a = 27; b = -86; c = -6;
Δ = b2-4ac
Δ = -862-4·27·(-6)
Δ = 8044
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:

$\sqrt{\Delta}=\sqrt{8044}=\sqrt{4*2011}=\sqrt{4}*\sqrt{2011}=2\sqrt{2011}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-86)-2\sqrt{2011}}{2*27}=\frac{86-2\sqrt{2011}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-86)+2\sqrt{2011}}{2*27}=\frac{86+2\sqrt{2011}}{54}
$