x^2-34x+16=0

Solution for x^2-34x+16=0 equation:

x^2-34x+16=0

a = 1; b = -34; c = +16;
Δ = b2-4ac
Δ = -342-4·1·16
Δ = 1092
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:

$\sqrt{\Delta}=\sqrt{1092}=\sqrt{4*273}=\sqrt{4}*\sqrt{273}=2\sqrt{273}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{273}}{2*1}=\frac{34-2\sqrt{273}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{273}}{2*1}=\frac{34+2\sqrt{273}}{2}
$