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6x^2+51x+100=0
a = 6; b = 51; c = +100;
Δ = b2-4ac
Δ = 512-4·6·100
Δ = 201
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-\sqrt{201}}{2*6}=\frac{-51-\sqrt{201}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+\sqrt{201}}{2*6}=\frac{-51+\sqrt{201}}{12} $
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