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6x^2+96x+378=0
a = 6; b = 96; c = +378;
Δ = b2-4ac
Δ = 962-4·6·378
Δ = 144
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{144}=12$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-12}{2*6}=\frac{-108}{12} =-9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+12}{2*6}=\frac{-84}{12} =-7 $
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