x^2-2x+34=177

Solution for x^2-2x+34=177 equation:

x^2-2x+34=177

We move all terms to the left:

x^2-2x+34-(177)=0

We add all the numbers together, and all the variables

x^2-2x-143=0

a = 1; b = -2; c = -143;
Δ = b2-4ac
Δ = -22-4·1·(-143)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-24}{2*1}=\frac{-22}{2}
=-11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+24}{2*1}=\frac{26}{2}
=13
$