x^2-38x+180.5=0

Solution for x^2-38x+180.5=0 equation:

x^2-38x+180.5=0

a = 1; b = -38; c = +180.5;
Δ = b2-4ac
Δ = -382-4·1·180.5
Δ = 722
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:

$\sqrt{\Delta}=\sqrt{722}=\sqrt{361*2}=\sqrt{361}*\sqrt{2}=19\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-19\sqrt{2}}{2*1}=\frac{38-19\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+19\sqrt{2}}{2*1}=\frac{38+19\sqrt{2}}{2}
$