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9y^2-184y+400=0
a = 9; b = -184; c = +400;
Δ = b2-4ac
Δ = -1842-4·9·400
Δ = 19456
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{19456}=\sqrt{1024*19}=\sqrt{1024}*\sqrt{19}=32\sqrt{19}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-184)-32\sqrt{19}}{2*9}=\frac{184-32\sqrt{19}}{18} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-184)+32\sqrt{19}}{2*9}=\frac{184+32\sqrt{19}}{18} $
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