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15a^2-31a+15=0
a = 15; b = -31; c = +15;
Δ = b2-4ac
Δ = -312-4·15·15
Δ = 61
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-\sqrt{61}}{2*15}=\frac{31-\sqrt{61}}{30} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{61}}{2*15}=\frac{31+\sqrt{61}}{30} $
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