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27x^2-51x+20=0
a = 27; b = -51; c = +20;
Δ = b2-4ac
Δ = -512-4·27·20
Δ = 441
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{441}=21$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-21}{2*27}=\frac{30}{54} =5/9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+21}{2*27}=\frac{72}{54} =1+1/3 $
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