5y^2-32y-36=0

Solution for 5y^2-32y-36=0 equation:

5y^2-32y-36=0

a = 5; b = -32; c = -36;
Δ = b2-4ac
Δ = -322-4·5·(-36)
Δ = 1744
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:

$\sqrt{\Delta}=\sqrt{1744}=\sqrt{16*109}=\sqrt{16}*\sqrt{109}=4\sqrt{109}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{109}}{2*5}=\frac{32-4\sqrt{109}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{109}}{2*5}=\frac{32+4\sqrt{109}}{10}
$