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2y^2-5y-24=0
a = 2; b = -5; c = -24;
Δ = b2-4ac
Δ = -52-4·2·(-24)
Δ = 217
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{217}}{2*2}=\frac{5-\sqrt{217}}{4} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{217}}{2*2}=\frac{5+\sqrt{217}}{4} $
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