x2-16x+37=0

Solution for x2-16x+37=0 equation:

x2-16x+37=0

We add all the numbers together, and all the variables

x^2-16x+37=0

a = 1; b = -16; c = +37;
Δ = b2-4ac
Δ = -162-4·1·37
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-6\sqrt{3}}{2*1}=\frac{16-6\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+6\sqrt{3}}{2*1}=\frac{16+6\sqrt{3}}{2}
$