3(x2-2)=6(x+4)

Solution for 3(x2-2)=6(x+4) equation:

3(x2-2)=6(x+4)

We move all terms to the left:

3(x2-2)-(6(x+4))=0

We add all the numbers together, and all the variables

3(+x^2-2)-(6(x+4))=0

We multiply parentheses

3x^2-(6(x+4))-6=0


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

6(x+4)

We multiply parentheses

6x+24

Back to the equation:

-(6x+24)


We get rid of parentheses

3x^2-6x-24-6=0

We add all the numbers together, and all the variables

3x^2-6x-30=0

a = 3; b = -6; c = -30;
Δ = b2-4ac
Δ = -62-4·3·(-30)
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{11}}{2*3}=\frac{6-6\sqrt{11}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{11}}{2*3}=\frac{6+6\sqrt{11}}{6}
$