y+6=17/y=11

Solution for y+6=17/y=11 equation:

y+6=17/y=11

We move all terms to the left:

y+6-(17/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-(+17/y)+6=0

We get rid of parentheses

y-17/y+6=0

We multiply all the terms by the denominator


y*y+6*y-17=0

We add all the numbers together, and all the variables

6y+y*y-17=0

Wy multiply elements

y^2+6y-17=0

a = 1; b = 6; c = -17;
Δ = b2-4ac
Δ = 62-4·1·(-17)
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{-(6)-2\sqrt{26}}{2*1}=\frac{-6-2\sqrt{26}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{26}}{2*1}=\frac{-6+2\sqrt{26}}{2}
$