5y(2y+1)=65

Solution for 5y(2y+1)=65 equation:

5y(2y+1)=65

We move all terms to the left:

5y(2y+1)-(65)=0

We multiply parentheses

10y^2+5y-65=0

a = 10; b = 5; c = -65;
Δ = b2-4ac
Δ = 52-4·10·(-65)
Δ = 2625
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:

$\sqrt{\Delta}=\sqrt{2625}=\sqrt{25*105}=\sqrt{25}*\sqrt{105}=5\sqrt{105}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{105}}{2*10}=\frac{-5-5\sqrt{105}}{20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{105}}{2*10}=\frac{-5+5\sqrt{105}}{20}
$