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12x^2-34x-6=0
a = 12; b = -34; c = -6;
Δ = b2-4ac
Δ = -342-4·12·(-6)
Δ = 1444
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{1444}=38$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-38}{2*12}=\frac{-4}{24} =-1/6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+38}{2*12}=\frac{72}{24} =3 $
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