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25y^2-50y-91=0
a = 25; b = -50; c = -91;
Δ = b2-4ac
Δ = -502-4·25·(-91)
Δ = 11600
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{11600}=\sqrt{400*29}=\sqrt{400}*\sqrt{29}=20\sqrt{29}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-20\sqrt{29}}{2*25}=\frac{50-20\sqrt{29}}{50} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+20\sqrt{29}}{2*25}=\frac{50+20\sqrt{29}}{50} $
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