X^2-16x+38=0

Solution for X^2-16x+38=0 equation:

X^2-16X+38=0

a = 1; b = -16; c = +38;
Δ = b2-4ac
Δ = -162-4·1·38
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{26}}{2*1}=\frac{16-2\sqrt{26}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{26}}{2*1}=\frac{16+2\sqrt{26}}{2}
$