y^2-10y-125=0

Solution for y^2-10y-125=0 equation:

y^2-10y-125=0

a = 1; b = -10; c = -125;
Δ = b2-4ac
Δ = -102-4·1·(-125)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{6}}{2*1}=\frac{10-10\sqrt{6}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{6}}{2*1}=\frac{10+10\sqrt{6}}{2}
$