b^2-34b+103=0

Solution for b^2-34b+103=0 equation:

b^2-34b+103=0

a = 1; b = -34; c = +103;
Δ = b2-4ac
Δ = -342-4·1·103
Δ = 744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{744}=\sqrt{4*186}=\sqrt{4}*\sqrt{186}=2\sqrt{186}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{186}}{2*1}=\frac{34-2\sqrt{186}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{186}}{2*1}=\frac{34+2\sqrt{186}}{2}
$