y^2-16y-71=0

Solution for y^2-16y-71=0 equation:

y^2-16y-71=0

a = 1; b = -16; c = -71;
Δ = b2-4ac
Δ = -162-4·1·(-71)
Δ = 540
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:

$\sqrt{\Delta}=\sqrt{540}=\sqrt{36*15}=\sqrt{36}*\sqrt{15}=6\sqrt{15}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-6\sqrt{15}}{2*1}=\frac{16-6\sqrt{15}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+6\sqrt{15}}{2*1}=\frac{16+6\sqrt{15}}{2}
$