3x(3x-6)=8

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Solution for 3x(3x-6)=8 equation:



3x(3x-6)=8
We move all terms to the left:
3x(3x-6)-(8)=0
We multiply parentheses
9x^2-18x-8=0
a = 9; b = -18; c = -8;
Δ = b2-4ac
Δ = -182-4·9·(-8)
Δ = 612
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:
$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{17}}{2*9}=\frac{18-6\sqrt{17}}{18} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{17}}{2*9}=\frac{18+6\sqrt{17}}{18} $

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