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-6x^2-5x+11=0
a = -6; b = -5; c = +11;
Δ = b2-4ac
Δ = -52-4·(-6)·11
Δ = 289
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{289}=17$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-17}{2*-6}=\frac{-12}{-12} =1 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+17}{2*-6}=\frac{22}{-12} =-1+5/6 $
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