3x^2-12x-129=0

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Solution for 3x^2-12x-129=0 equation:



3x^2-12x-129=0
a = 3; b = -12; c = -129;
Δ = b2-4ac
Δ = -122-4·3·(-129)
Δ = 1692
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:
$\sqrt{\Delta}=\sqrt{1692}=\sqrt{36*47}=\sqrt{36}*\sqrt{47}=6\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{47}}{2*3}=\frac{12-6\sqrt{47}}{6} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{47}}{2*3}=\frac{12+6\sqrt{47}}{6} $

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