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6x^2-33x+42=0
a = 6; b = -33; c = +42;
Δ = b2-4ac
Δ = -332-4·6·42
Δ = 81
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{81}=9$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-9}{2*6}=\frac{24}{12} =2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+9}{2*6}=\frac{42}{12} =3+1/2 $
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