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6x(54-x)=18
We move all terms to the left:
6x(54-x)-(18)=0
We add all the numbers together, and all the variables
6x(-1x+54)-18=0
We multiply parentheses
-6x^2+324x-18=0
a = -6; b = 324; c = -18;
Δ = b2-4ac
Δ = 3242-4·(-6)·(-18)
Δ = 104544
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{104544}=\sqrt{17424*6}=\sqrt{17424}*\sqrt{6}=132\sqrt{6}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(324)-132\sqrt{6}}{2*-6}=\frac{-324-132\sqrt{6}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(324)+132\sqrt{6}}{2*-6}=\frac{-324+132\sqrt{6}}{-12} $
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