Y^3-15y^2+75=y-125

Solution for Y^3-15y^2+75=y-125 equation:

^3-15Y^2+75=Y-125

We move all terms to the left:

^3-15Y^2+75-(Y-125)=0

We add all the numbers together, and all the variables

-15Y^2-(Y-125)=0

We get rid of parentheses

-15Y^2-Y+125=0

We add all the numbers together, and all the variables

-15Y^2-1Y+125=0

a = -15; b = -1; c = +125;
Δ = b2-4ac
Δ = -12-4·(-15)·125
Δ = 7501
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{7501}}{2*-15}=\frac{1-\sqrt{7501}}{-30}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{7501}}{2*-15}=\frac{1+\sqrt{7501}}{-30}
$