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9x^2-31x=51
We move all terms to the left:
9x^2-31x-(51)=0
a = 9; b = -31; c = -51;
Δ = b2-4ac
Δ = -312-4·9·(-51)
Δ = 2797
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-\sqrt{2797}}{2*9}=\frac{31-\sqrt{2797}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{2797}}{2*9}=\frac{31+\sqrt{2797}}{18} $
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