-2y(y-3)+5=3

Solution for -2y(y-3)+5=3 equation:

-2y(y-3)+5=3

We move all terms to the left:

-2y(y-3)+5-(3)=0

We add all the numbers together, and all the variables

-2y(y-3)+2=0

We multiply parentheses

-2y^2+6y+2=0

a = -2; b = 6; c = +2;
Δ = b2-4ac
Δ = 62-4·(-2)·2
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{13}}{2*-2}=\frac{-6-2\sqrt{13}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{13}}{2*-2}=\frac{-6+2\sqrt{13}}{-4}
$