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14x^2-31x+15=0
a = 14; b = -31; c = +15;
Δ = b2-4ac
Δ = -312-4·14·15
Δ = 121
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{121}=11$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-11}{2*14}=\frac{20}{28} =5/7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+11}{2*14}=\frac{42}{28} =1+1/2 $
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