y^2-14y+31=0

Solution for y^2-14y+31=0 equation:

y^2-14y+31=0

a = 1; b = -14; c = +31;
Δ = b2-4ac
Δ = -142-4·1·31
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6\sqrt{2}}{2*1}=\frac{14-6\sqrt{2}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6\sqrt{2}}{2*1}=\frac{14+6\sqrt{2}}{2}
$