3x(x-3)=9

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Solution for 3x(x-3)=9 equation:



3x(x-3)=9
We move all terms to the left:
3x(x-3)-(9)=0
We multiply parentheses
3x^2-9x-9=0
a = 3; b = -9; c = -9;
Δ = b2-4ac
Δ = -92-4·3·(-9)
Δ = 189
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:
$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{21}}{2*3}=\frac{9-3\sqrt{21}}{6} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{21}}{2*3}=\frac{9+3\sqrt{21}}{6} $

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