65-3y=2y^2

Solution for 65-3y=2y^2 equation:

65-3y=2y^2

We move all terms to the left:

65-3y-(2y^2)=0

determiningTheFunctionDomain
-2y^2-3y+65=0

a = -2; b = -3; c = +65;
Δ = b2-4ac
Δ = -32-4·(-2)·65
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-23}{2*-2}=\frac{-20}{-4}
=+5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+23}{2*-2}=\frac{26}{-4}
=-6+1/2
$