y^2=10y+25=0

Solution for y^2=10y+25=0 equation:

y^2=10y+25=0

We move all terms to the left:

y^2-(10y+25)=0

We get rid of parentheses

y^2-10y-25=0

a = 1; b = -10; c = -25;
Δ = b2-4ac
Δ = -102-4·1·(-25)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{2}}{2*1}=\frac{10-10\sqrt{2}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{2}}{2*1}=\frac{10+10\sqrt{2}}{2}
$