25y^2+10y-71=0

Solution for 25y^2+10y-71=0 equation:

25y^2+10y-71=0

a = 25; b = 10; c = -71;
Δ = b2-4ac
Δ = 102-4·25·(-71)
Δ = 7200
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:

$\sqrt{\Delta}=\sqrt{7200}=\sqrt{3600*2}=\sqrt{3600}*\sqrt{2}=60\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-60\sqrt{2}}{2*25}=\frac{-10-60\sqrt{2}}{50}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+60\sqrt{2}}{2*25}=\frac{-10+60\sqrt{2}}{50}
$