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6x^2-17x-45=0
a = 6; b = -17; c = -45;
Δ = b2-4ac
Δ = -172-4·6·(-45)
Δ = 1369
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{1369}=37x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-37}{2*6}=\frac{-20}{12} =-1+2/3x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+37}{2*6}=\frac{54}{12} =4+1/2
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