8=3(3x+8)x

Solution for 8=3(3x+8)x equation:

8=3(3x+8)x

We move all terms to the left:

8-(3(3x+8)x)=0


We calculate terms in parentheses: -(3(3x+8)x), so:

3(3x+8)x

We multiply parentheses

9x^2+24x

Back to the equation:

-(9x^2+24x)


We get rid of parentheses

-9x^2-24x+8=0

a = -9; b = -24; c = +8;
Δ = b2-4ac
Δ = -242-4·(-9)·8
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{6}}{2*-9}=\frac{24-12\sqrt{6}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{6}}{2*-9}=\frac{24+12\sqrt{6}}{-18}
$