4225-130y+y^2+520-8y+y^2-16y=4289

Solution for 4225-130y+y^2+520-8y+y^2-16y=4289 equation:

4225-130y+y^2+520-8y+y^2-16y=4289

We move all terms to the left:

4225-130y+y^2+520-8y+y^2-16y-(4289)=0

We add all the numbers together, and all the variables

2y^2-154y+456=0

a = 2; b = -154; c = +456;
Δ = b2-4ac
Δ = -1542-4·2·456
Δ = 20068
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20068}=\sqrt{4*5017}=\sqrt{4}*\sqrt{5017}=2\sqrt{5017}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-154)-2\sqrt{5017}}{2*2}=\frac{154-2\sqrt{5017}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-154)+2\sqrt{5017}}{2*2}=\frac{154+2\sqrt{5017}}{4}
$