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y^2-80y+15=0
a = 1; b = -80; c = +15;
Δ = b2-4ac
Δ = -802-4·1·15
Δ = 6340
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6340}=\sqrt{4*1585}=\sqrt{4}*\sqrt{1585}=2\sqrt{1585}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-2\sqrt{1585}}{2*1}=\frac{80-2\sqrt{1585}}{2} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+2\sqrt{1585}}{2*1}=\frac{80+2\sqrt{1585}}{2} $
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