9x(2x-3)=12x+4+6x

Solution for 9x(2x-3)=12x+4+6x equation:

9x(2x-3)=12x+4+6x

We move all terms to the left:

9x(2x-3)-(12x+4+6x)=0

We add all the numbers together, and all the variables

9x(2x-3)-(18x+4)=0

We multiply parentheses

18x^2-27x-(18x+4)=0

We get rid of parentheses

18x^2-27x-18x-4=0

We add all the numbers together, and all the variables

18x^2-45x-4=0

a = 18; b = -45; c = -4;
Δ = b2-4ac
Δ = -452-4·18·(-4)
Δ = 2313
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:

$\sqrt{\Delta}=\sqrt{2313}=\sqrt{9*257}=\sqrt{9}*\sqrt{257}=3\sqrt{257}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{257}}{2*18}=\frac{45-3\sqrt{257}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{257}}{2*18}=\frac{45+3\sqrt{257}}{36}
$