Y=55/x-x

Solution for Y=55/x-x equation:

=55/Y-Y

We move all terms to the left:

-(55/Y-Y)=0


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

Y∈R


We add all the numbers together, and all the variables

-(-1Y+55/Y)=0

We get rid of parentheses

1Y-55/Y=0

We multiply all the terms by the denominator


1Y*Y-55=0

Wy multiply elements

Y^2-55=0

a = 1; b = 0; c = -55;
Δ = b2-4ac
Δ = 02-4·1·(-55)
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{55}}{2*1}=\frac{0-2\sqrt{55}}{2}
=-\frac{2\sqrt{55}}{2}
=-\sqrt{55}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{55}}{2*1}=\frac{0+2\sqrt{55}}{2}
=\frac{2\sqrt{55}}{2}
=\sqrt{55}
$