X^2-6x+34=105

Solution for X^2-6x+34=105 equation:

X^2-6X+34=105

We move all terms to the left:

X^2-6X+34-(105)=0

We add all the numbers together, and all the variables

X^2-6X-71=0

a = 1; b = -6; c = -71;
Δ = b2-4ac
Δ = -62-4·1·(-71)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-8\sqrt{5}}{2*1}=\frac{6-8\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+8\sqrt{5}}{2*1}=\frac{6+8\sqrt{5}}{2}
$