y(5y-12)=17

Solution for y(5y-12)=17 equation:

y(5y-12)=17

We move all terms to the left:

y(5y-12)-(17)=0

We multiply parentheses

5y^2-12y-17=0

a = 5; b = -12; c = -17;
Δ = b2-4ac
Δ = -122-4·5·(-17)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-22}{2*5}=\frac{-10}{10}
=-1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+22}{2*5}=\frac{34}{10}
=3+2/5
$