24y^2+80y+25=0

Solution for 24y^2+80y+25=0 equation:

24y^2+80y+25=0

a = 24; b = 80; c = +25;
Δ = b2-4ac
Δ = 802-4·24·25
Δ = 4000
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:

$\sqrt{\Delta}=\sqrt{4000}=\sqrt{400*10}=\sqrt{400}*\sqrt{10}=20\sqrt{10}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-20\sqrt{10}}{2*24}=\frac{-80-20\sqrt{10}}{48}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+20\sqrt{10}}{2*24}=\frac{-80+20\sqrt{10}}{48}
$