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6x^2-59x+45=0
a = 6; b = -59; c = +45;
Δ = b2-4ac
Δ = -592-4·6·45
Δ = 2401
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{2401}=49$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-49}{2*6}=\frac{10}{12} =5/6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+49}{2*6}=\frac{108}{12} =9 $
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