5y^2-12y-13=0

Solution for 5y^2-12y-13=0 equation:

5y^2-12y-13=0

a = 5; b = -12; c = -13;
Δ = b2-4ac
Δ = -122-4·5·(-13)
Δ = 404
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:

$\sqrt{\Delta}=\sqrt{404}=\sqrt{4*101}=\sqrt{4}*\sqrt{101}=2\sqrt{101}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{101}}{2*5}=\frac{12-2\sqrt{101}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{101}}{2*5}=\frac{12+2\sqrt{101}}{10}
$