2y^2+3y=65

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

2y^2+3y=65

We move all terms to the left:

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