X(x+2x)=8(8+x+4)

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

X(X+2X)=8(8+X+4)

We move all terms to the left:

X(X+2X)-(8(8+X+4))=0

We add all the numbers together, and all the variables

X(+3X)-(8(X+12))=0

We multiply parentheses

3X^2-(8(X+12))=0


We calculate terms in parentheses: -(8(X+12)), so:

8(X+12)

We multiply parentheses

8X+96

Back to the equation:

-(8X+96)


We get rid of parentheses

3X^2-8X-96=0

a = 3; b = -8; c = -96;
Δ = b2-4ac
Δ = -82-4·3·(-96)
Δ = 1216
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:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{19}}{2*3}=\frac{8-8\sqrt{19}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{19}}{2*3}=\frac{8+8\sqrt{19}}{6}
$