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6x^2-45x+54=0
a = 6; b = -45; c = +54;
Δ = b2-4ac
Δ = -452-4·6·54
Δ = 729
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{729}=27$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-27}{2*6}=\frac{18}{12} =1+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+27}{2*6}=\frac{72}{12} =6 $
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