2y^2-5y=3y+64

Solution for 2y^2-5y=3y+64 equation:

2y^2-5y=3y+64

We move all terms to the left:

2y^2-5y-(3y+64)=0

We get rid of parentheses

2y^2-5y-3y-64=0

We add all the numbers together, and all the variables

2y^2-8y-64=0

a = 2; b = -8; c = -64;
Δ = b2-4ac
Δ = -82-4·2·(-64)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-24}{2*2}=\frac{-16}{4}
=-4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+24}{2*2}=\frac{32}{4}
=8
$