5y^2+125y+50=0

Solution for 5y^2+125y+50=0 equation:

5y^2+125y+50=0

a = 5; b = 125; c = +50;
Δ = b2-4ac
Δ = 1252-4·5·50
Δ = 14625
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:

$\sqrt{\Delta}=\sqrt{14625}=\sqrt{225*65}=\sqrt{225}*\sqrt{65}=15\sqrt{65}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(125)-15\sqrt{65}}{2*5}=\frac{-125-15\sqrt{65}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(125)+15\sqrt{65}}{2*5}=\frac{-125+15\sqrt{65}}{10}
$