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

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

3X(2X-3)-9X-4=2X+12

We move all terms to the left:

3X(2X-3)-9X-4-(2X+12)=0

We add all the numbers together, and all the variables

-9X+3X(2X-3)-(2X+12)-4=0

We multiply parentheses

6X^2-9X-9X-(2X+12)-4=0

We get rid of parentheses

6X^2-9X-9X-2X-12-4=0

We add all the numbers together, and all the variables

6X^2-20X-16=0

a = 6; b = -20; c = -16;
Δ = b2-4ac
Δ = -202-4·6·(-16)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-28}{2*6}=\frac{-8}{12}
=-2/3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+28}{2*6}=\frac{48}{12}
=4
$