5y^2+18y-127=0

Solution for 5y^2+18y-127=0 equation:

5y^2+18y-127=0

a = 5; b = 18; c = -127;
Δ = b2-4ac
Δ = 182-4·5·(-127)
Δ = 2864
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:

$\sqrt{\Delta}=\sqrt{2864}=\sqrt{16*179}=\sqrt{16}*\sqrt{179}=4\sqrt{179}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-4\sqrt{179}}{2*5}=\frac{-18-4\sqrt{179}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+4\sqrt{179}}{2*5}=\frac{-18+4\sqrt{179}}{10}
$