y^2-22y+10=0

Solution for y^2-22y+10=0 equation:

y^2-22y+10=0

a = 1; b = -22; c = +10;
Δ = b2-4ac
Δ = -222-4·1·10
Δ = 444
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:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{111}}{2*1}=\frac{22-2\sqrt{111}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{111}}{2*1}=\frac{22+2\sqrt{111}}{2}
$