Y^3-5=y-45y^2

Solution for Y^3-5=y-45y^2 equation:

^3-5=Y-45Y^2

We move all terms to the left:

^3-5-(Y-45Y^2)=0

We add all the numbers together, and all the variables

-(Y-45Y^2)=0

We get rid of parentheses

45Y^2-Y=0

We add all the numbers together, and all the variables

45Y^2-1Y=0

a = 45; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·45·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*45}=\frac{0}{90}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*45}=\frac{2}{90}
=1/45
$