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6x^2-118x-120=0
a = 6; b = -118; c = -120;
Δ = b2-4ac
Δ = -1182-4·6·(-120)
Δ = 16804
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{16804}=\sqrt{4*4201}=\sqrt{4}*\sqrt{4201}=2\sqrt{4201}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-118)-2\sqrt{4201}}{2*6}=\frac{118-2\sqrt{4201}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-118)+2\sqrt{4201}}{2*6}=\frac{118+2\sqrt{4201}}{12} $
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