17/y-y=10

Solution for 17/y-y=10 equation:

17/y-y=10

We move all terms to the left:

17/y-y-(10)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

-1y+17/y-10=0

We multiply all the terms by the denominator


-1y*y-10*y+17=0

We add all the numbers together, and all the variables

-10y-1y*y+17=0

Wy multiply elements

-1y^2-10y+17=0

a = -1; b = -10; c = +17;
Δ = b2-4ac
Δ = -102-4·(-1)·17
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{42}}{2*-1}=\frac{10-2\sqrt{42}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{42}}{2*-1}=\frac{10+2\sqrt{42}}{-2}
$