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6x^2-84x+6=0
a = 6; b = -84; c = +6;
Δ = b2-4ac
Δ = -842-4·6·6
Δ = 6912
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6912}=\sqrt{2304*3}=\sqrt{2304}*\sqrt{3}=48\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-48\sqrt{3}}{2*6}=\frac{84-48\sqrt{3}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+48\sqrt{3}}{2*6}=\frac{84+48\sqrt{3}}{12} $
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