169=y^2-6y+34

Solution for 169=y^2-6y+34 equation:

169=y^2-6y+34

We move all terms to the left:

169-(y^2-6y+34)=0

We get rid of parentheses

-y^2+6y-34+169=0

We add all the numbers together, and all the variables

-1y^2+6y+135=0

a = -1; b = 6; c = +135;
Δ = b2-4ac
Δ = 62-4·(-1)·135
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-24}{2*-1}=\frac{-30}{-2}
=+15
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+24}{2*-1}=\frac{18}{-2}
=-9
$