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6x^2-78x-84=0
a = 6; b = -78; c = -84;
Δ = b2-4ac
Δ = -782-4·6·(-84)
Δ = 8100
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{8100}=90$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-90}{2*6}=\frac{-12}{12} =-1 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+90}{2*6}=\frac{168}{12} =14 $
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