529+y^2=509+10y

Solution for 529+y^2=509+10y equation:

529+y^2=509+10y

We move all terms to the left:

529+y^2-(509+10y)=0

We add all the numbers together, and all the variables

y^2-(10y+509)+529=0

We get rid of parentheses

y^2-10y-509+529=0

We add all the numbers together, and all the variables

y^2-10y+20=0

a = 1; b = -10; c = +20;
Δ = b2-4ac
Δ = -102-4·1·20
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{5}}{2*1}=\frac{10-2\sqrt{5}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{5}}{2*1}=\frac{10+2\sqrt{5}}{2}
$