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6x(x-2)=54
We move all terms to the left:
6x(x-2)-(54)=0
We multiply parentheses
6x^2-12x-54=0
a = 6; b = -12; c = -54;
Δ = b2-4ac
Δ = -122-4·6·(-54)
Δ = 1440
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{10}}{2*6}=\frac{12-12\sqrt{10}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{10}}{2*6}=\frac{12+12\sqrt{10}}{12} $
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