x^2-17x+17.25=0

Solution for x^2-17x+17.25=0 equation:

x^2-17x+17.25=0

a = 1; b = -17; c = +17.25;
Δ = b2-4ac
Δ = -172-4·1·17.25
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-2\sqrt{55}}{2*1}=\frac{17-2\sqrt{55}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+2\sqrt{55}}{2*1}=\frac{17+2\sqrt{55}}{2}
$