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6x^2-12x=21
We move all terms to the left:
6x^2-12x-(21)=0
a = 6; b = -12; c = -21;
Δ = b2-4ac
Δ = -122-4·6·(-21)
Δ = 648
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-18\sqrt{2}}{2*6}=\frac{12-18\sqrt{2}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+18\sqrt{2}}{2*6}=\frac{12+18\sqrt{2}}{12} $
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