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6x^2+57x+126=0
a = 6; b = 57; c = +126;
Δ = b2-4ac
Δ = 572-4·6·126
Δ = 225
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{225}=15$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-15}{2*6}=\frac{-72}{12} =-6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+15}{2*6}=\frac{-42}{12} =-3+1/2 $
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