3x(2x+3)=2x+9

Solution for 3x(2x+3)=2x+9 equation:

3x(2x+3)=2x+9

We move all terms to the left:

3x(2x+3)-(2x+9)=0

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

6x^2+7x-9=0

a = 6; b = 7; c = -9;
Δ = b2-4ac
Δ = 72-4·6·(-9)
Δ = 265
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{265}}{2*6}=\frac{-7-\sqrt{265}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{265}}{2*6}=\frac{-7+\sqrt{265}}{12}
$