25y+y^2-100=0

Solution for 25y+y^2-100=0 equation:

25y+y^2-100=0

a = 1; b = 25; c = -100;
Δ = b2-4ac
Δ = 252-4·1·(-100)
Δ = 1025
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:

$\sqrt{\Delta}=\sqrt{1025}=\sqrt{25*41}=\sqrt{25}*\sqrt{41}=5\sqrt{41}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-5\sqrt{41}}{2*1}=\frac{-25-5\sqrt{41}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+5\sqrt{41}}{2*1}=\frac{-25+5\sqrt{41}}{2}
$