x(3x-6)=340

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Solution for x(3x-6)=340 equation:



x(3x-6)=340
We move all terms to the left:
x(3x-6)-(340)=0
We multiply parentheses
3x^2-6x-340=0
a = 3; b = -6; c = -340;
Δ = b2-4ac
Δ = -62-4·3·(-340)
Δ = 4116
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:
$\sqrt{\Delta}=\sqrt{4116}=\sqrt{196*21}=\sqrt{196}*\sqrt{21}=14\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-14\sqrt{21}}{2*3}=\frac{6-14\sqrt{21}}{6} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+14\sqrt{21}}{2*3}=\frac{6+14\sqrt{21}}{6} $

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