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-6x^2+9x+42=0
a = -6; b = 9; c = +42;
Δ = b2-4ac
Δ = 92-4·(-6)·42
Δ = 1089
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{1089}=33$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-33}{2*-6}=\frac{-42}{-12} =3+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+33}{2*-6}=\frac{24}{-12} =-2 $
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