4-3y(y-4/y)=41-y^2

Solution for 4-3y(y-4/y)=41-y^2 equation:

4-3y(y-4/y)=41-y^2

We move all terms to the left:

4-3y(y-4/y)-(41-y^2)=0


Domain of the equation: y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

-(41-y^2)-3y(+y-4/y)+4=0

We multiply parentheses

-(41-y^2)-3y^2+12y^2+4=0

We get rid of parentheses

y^2-3y^2+12y^2-41+4=0

We add all the numbers together, and all the variables

10y^2-37=0

a = 10; b = 0; c = -37;
Δ = b2-4ac
Δ = 02-4·10·(-37)
Δ = 1480
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:

$\sqrt{\Delta}=\sqrt{1480}=\sqrt{4*370}=\sqrt{4}*\sqrt{370}=2\sqrt{370}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{370}}{2*10}=\frac{0-2\sqrt{370}}{20}
=-\frac{2\sqrt{370}}{20}
=-\frac{\sqrt{370}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{370}}{2*10}=\frac{0+2\sqrt{370}}{20}
=\frac{2\sqrt{370}}{20}
=\frac{\sqrt{370}}{10}
$