250/y-3*y=55

Solution for 250/y-3*y=55 equation:

250/y-3y=55

We move all terms to the left:

250/y-3y-(55)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

-3y+250/y-55=0

We multiply all the terms by the denominator


-3y*y-55*y+250=0

We add all the numbers together, and all the variables

-55y-3y*y+250=0

Wy multiply elements

-3y^2-55y+250=0

a = -3; b = -55; c = +250;
Δ = b2-4ac
Δ = -552-4·(-3)·250
Δ = 6025
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:

$\sqrt{\Delta}=\sqrt{6025}=\sqrt{25*241}=\sqrt{25}*\sqrt{241}=5\sqrt{241}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-5\sqrt{241}}{2*-3}=\frac{55-5\sqrt{241}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+5\sqrt{241}}{2*-3}=\frac{55+5\sqrt{241}}{-6}
$