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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

6(4x+2)

We multiply parentheses

24x+12

Back to the equation:

-(24x+12)


We get rid of parentheses

3x^2+24x-24x-12=0

We add all the numbers together, and all the variables

3x^2-12=0

a = 3; b = 0; c = -12;
Δ = b2-4ac
Δ = 02-4·3·(-12)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*3}=\frac{-12}{6}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*3}=\frac{12}{6}
=2
$