Y=x-26/x

Solution for Y=x-26/x equation:

=Y-26/Y

We move all terms to the left:

-(Y-26/Y)=0


Domain of the equation: Y)!=0

Y!=0/1

Y!=0

Y∈R


We add all the numbers together, and all the variables

-(+Y-26/Y)=0

We get rid of parentheses

-Y+26/Y=0

We multiply all the terms by the denominator


-Y*Y+26=0

Wy multiply elements

-1Y^2+26=0

a = -1; b = 0; c = +26;
Δ = b2-4ac
Δ = 02-4·(-1)·26
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{26}}{2*-1}=\frac{0-2\sqrt{26}}{-2}
=-\frac{2\sqrt{26}}{-2}
=-\frac{\sqrt{26}}{-1}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{26}}{2*-1}=\frac{0+2\sqrt{26}}{-2}
=\frac{2\sqrt{26}}{-2}
=\frac{\sqrt{26}}{-1}
$