3(x+8)+3x=6(x-2)4x+9

Solution for 3(x+8)+3x=6(x-2)4x+9 equation:

3(x+8)+3x=6(x-2)4x+9

We move all terms to the left:

3(x+8)+3x-(6(x-2)4x+9)=0

We add all the numbers together, and all the variables

3x+3(x+8)-(6(x-2)4x+9)=0

We multiply parentheses

3x+3x-(6(x-2)4x+9)+24=0


We calculate terms in parentheses: -(6(x-2)4x+9), so:

6(x-2)4x+9

We multiply parentheses

24x^2-48x+9

Back to the equation:

-(24x^2-48x+9)


We add all the numbers together, and all the variables

6x-(24x^2-48x+9)+24=0

We get rid of parentheses

-24x^2+6x+48x-9+24=0

We add all the numbers together, and all the variables

-24x^2+54x+15=0

a = -24; b = 54; c = +15;
Δ = b2-4ac
Δ = 542-4·(-24)·15
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-66}{2*-24}=\frac{-120}{-48}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+66}{2*-24}=\frac{12}{-48}
=-1/4
$