5y^2-12y-27=0

Solution for 5y^2-12y-27=0 equation:

5y^2-12y-27=0

a = 5; b = -12; c = -27;
Δ = b2-4ac
Δ = -122-4·5·(-27)
Δ = 684
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:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{19}}{2*5}=\frac{12-6\sqrt{19}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{19}}{2*5}=\frac{12+6\sqrt{19}}{10}
$