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9(x-4)3x=18
We move all terms to the left:
9(x-4)3x-(18)=0
We multiply parentheses
27x^2-108x-18=0
a = 27; b = -108; c = -18;
Δ = b2-4ac
Δ = -1082-4·27·(-18)
Δ = 13608
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{13608}=\sqrt{324*42}=\sqrt{324}*\sqrt{42}=18\sqrt{42}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-18\sqrt{42}}{2*27}=\frac{108-18\sqrt{42}}{54} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+18\sqrt{42}}{2*27}=\frac{108+18\sqrt{42}}{54} $
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