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9y^2-12y-14=0
a = 9; b = -12; c = -14;
Δ = b2-4ac
Δ = -122-4·9·(-14)
Δ = 648
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-18\sqrt{2}}{2*9}=\frac{12-18\sqrt{2}}{18} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+18\sqrt{2}}{2*9}=\frac{12+18\sqrt{2}}{18} $
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