y-8/9y=11

Solution for y-8/9y=11 equation:

y-8/9y=11

We move all terms to the left:

y-8/9y-(11)=0


Domain of the equation: 9y!=0

y!=0/9

y!=0

y∈R


We multiply all the terms by the denominator


y*9y-11*9y-8=0

Wy multiply elements

9y^2-99y-8=0

a = 9; b = -99; c = -8;
Δ = b2-4ac
Δ = -992-4·9·(-8)
Δ = 10089
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:

$\sqrt{\Delta}=\sqrt{10089}=\sqrt{9*1121}=\sqrt{9}*\sqrt{1121}=3\sqrt{1121}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-99)-3\sqrt{1121}}{2*9}=\frac{99-3\sqrt{1121}}{18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+3\sqrt{1121}}{2*9}=\frac{99+3\sqrt{1121}}{18}
$