5y(y-3)=19

Solution for 5y(y-3)=19 equation:

5y(y-3)=19

We move all terms to the left:

5y(y-3)-(19)=0

We multiply parentheses

5y^2-15y-19=0

a = 5; b = -15; c = -19;
Δ = b2-4ac
Δ = -152-4·5·(-19)
Δ = 605
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:

$\sqrt{\Delta}=\sqrt{605}=\sqrt{121*5}=\sqrt{121}*\sqrt{5}=11\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-11\sqrt{5}}{2*5}=\frac{15-11\sqrt{5}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+11\sqrt{5}}{2*5}=\frac{15+11\sqrt{5}}{10}
$