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6x(18-x)=54
We move all terms to the left:
6x(18-x)-(54)=0
We add all the numbers together, and all the variables
6x(-1x+18)-54=0
We multiply parentheses
-6x^2+108x-54=0
a = -6; b = 108; c = -54;
Δ = b2-4ac
Δ = 1082-4·(-6)·(-54)
Δ = 10368
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{10368}=\sqrt{5184*2}=\sqrt{5184}*\sqrt{2}=72\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-72\sqrt{2}}{2*-6}=\frac{-108-72\sqrt{2}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+72\sqrt{2}}{2*-6}=\frac{-108+72\sqrt{2}}{-12} $
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