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12x^2+31x+9=0
a = 12; b = 31; c = +9;
Δ = b2-4ac
Δ = 312-4·12·9
Δ = 529
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{529}=23$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-23}{2*12}=\frac{-54}{24} =-2+1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+23}{2*12}=\frac{-8}{24} =-1/3 $
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