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6x(x-1)=126
We move all terms to the left:
6x(x-1)-(126)=0
We multiply parentheses
6x^2-6x-126=0
a = 6; b = -6; c = -126;
Δ = b2-4ac
Δ = -62-4·6·(-126)
Δ = 3060
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3060}=\sqrt{36*85}=\sqrt{36}*\sqrt{85}=6\sqrt{85}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{85}}{2*6}=\frac{6-6\sqrt{85}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{85}}{2*6}=\frac{6+6\sqrt{85}}{12} $
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