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9y^2-69y-34=0
a = 9; b = -69; c = -34;
Δ = b2-4ac
Δ = -692-4·9·(-34)
Δ = 5985
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5985}=\sqrt{9*665}=\sqrt{9}*\sqrt{665}=3\sqrt{665}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-3\sqrt{665}}{2*9}=\frac{69-3\sqrt{665}}{18} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+3\sqrt{665}}{2*9}=\frac{69+3\sqrt{665}}{18} $
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