y^2-10y-31=0

Solution for y^2-10y-31=0 equation:

y^2-10y-31=0

a = 1; b = -10; c = -31;
Δ = b2-4ac
Δ = -102-4·1·(-31)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{14}}{2*1}=\frac{10-4\sqrt{14}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{14}}{2*1}=\frac{10+4\sqrt{14}}{2}
$