x^2-22x+71=0

Solution for x^2-22x+71=0 equation:

x^2-22x+71=0

a = 1; b = -22; c = +71;
Δ = b2-4ac
Δ = -222-4·1·71
Δ = 200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-10\sqrt{2}}{2*1}=\frac{22-10\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+10\sqrt{2}}{2*1}=\frac{22+10\sqrt{2}}{2}
$