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12x^2-22x-42=0
a = 12; b = -22; c = -42;
Δ = b2-4ac
Δ = -222-4·12·(-42)
Δ = 2500
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{2500}=50$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-50}{2*12}=\frac{-28}{24} =-1+1/6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+50}{2*12}=\frac{72}{24} =3 $
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