x^2-38*x+1=0

Solution for x^2-38*x+1=0 equation:

x^2-38x+1=0

a = 1; b = -38; c = +1;
Δ = b2-4ac
Δ = -382-4·1·1
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-12\sqrt{10}}{2*1}=\frac{38-12\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+12\sqrt{10}}{2*1}=\frac{38+12\sqrt{10}}{2}
$