Y^3=2y^2-63y

Solution for Y^3=2y^2-63y equation:

^3=2Y^2-63Y

We move all terms to the left:

^3-(2Y^2-63Y)=0

We add all the numbers together, and all the variables

-(2Y^2-63Y)=0

We get rid of parentheses

-2Y^2+63Y=0

a = -2; b = 63; c = 0;
Δ = b2-4ac
Δ = 632-4·(-2)·0
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-63}{2*-2}=\frac{-126}{-4}
=31+1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+63}{2*-2}=\frac{0}{-4}
=0
$