9x(x+8)=3x+6

Solution for 9x(x+8)=3x+6 equation:

9x(x+8)=3x+6

We move all terms to the left:

9x(x+8)-(3x+6)=0

We multiply parentheses

9x^2+72x-(3x+6)=0

We get rid of parentheses

9x^2+72x-3x-6=0

We add all the numbers together, and all the variables

9x^2+69x-6=0

a = 9; b = 69; c = -6;
Δ = b2-4ac
Δ = 692-4·9·(-6)
Δ = 4977
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:

$\sqrt{\Delta}=\sqrt{4977}=\sqrt{9*553}=\sqrt{9}*\sqrt{553}=3\sqrt{553}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(69)-3\sqrt{553}}{2*9}=\frac{-69-3\sqrt{553}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+3\sqrt{553}}{2*9}=\frac{-69+3\sqrt{553}}{18}
$