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12x^2-31x+14=0
a = 12; b = -31; c = +14;
Δ = b2-4ac
Δ = -312-4·12·14
Δ = 289
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{289}=17$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-17}{2*12}=\frac{14}{24} =7/12 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+17}{2*12}=\frac{48}{24} =2 $
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