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18x^2-6x-6x+2=120
We move all terms to the left:
18x^2-6x-6x+2-(120)=0
We add all the numbers together, and all the variables
18x^2-12x-118=0
a = 18; b = -12; c = -118;
Δ = b2-4ac
Δ = -122-4·18·(-118)
Δ = 8640
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8640}=\sqrt{576*15}=\sqrt{576}*\sqrt{15}=24\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-24\sqrt{15}}{2*18}=\frac{12-24\sqrt{15}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+24\sqrt{15}}{2*18}=\frac{12+24\sqrt{15}}{36} $
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