2y^2-5y=3y+63

Solution for 2y^2-5y=3y+63 equation:

2y^2-5y=3y+63

We move all terms to the left:

2y^2-5y-(3y+63)=0

We get rid of parentheses

2y^2-5y-3y-63=0

We add all the numbers together, and all the variables

2y^2-8y-63=0

a = 2; b = -8; c = -63;
Δ = b2-4ac
Δ = -82-4·2·(-63)
Δ = 568
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:

$\sqrt{\Delta}=\sqrt{568}=\sqrt{4*142}=\sqrt{4}*\sqrt{142}=2\sqrt{142}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{142}}{2*2}=\frac{8-2\sqrt{142}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{142}}{2*2}=\frac{8+2\sqrt{142}}{4}
$