(Y^3+5y^2-2y+24)/(y-2)=0

Solution for (Y^3+5y^2-2y+24)/(y-2)=0 equation:

(^3+5Y^2-2Y+24)/(Y-2)=0


Domain of the equation: (Y-2)!=0

We move all terms containing Y to the left, all other terms to the right

Y!=2

Y∈R


We multiply all the terms by the denominator


(^3+5Y^2-2Y+24)=0

We get rid of parentheses

5Y^2-2Y+24+^3=0

We add all the numbers together, and all the variables

5Y^2-2Y=0

a = 5; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·5·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*5}=\frac{0}{10}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*5}=\frac{4}{10}
=2/5
$