y-8/9y=24

Solution for y-8/9y=24 equation:

y-8/9y=24

We move all terms to the left:

y-8/9y-(24)=0


Domain of the equation: 9y!=0

y!=0/9

y!=0

y∈R


We multiply all the terms by the denominator


y*9y-24*9y-8=0

Wy multiply elements

9y^2-216y-8=0

a = 9; b = -216; c = -8;
Δ = b2-4ac
Δ = -2162-4·9·(-8)
Δ = 46944
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:

$\sqrt{\Delta}=\sqrt{46944}=\sqrt{144*326}=\sqrt{144}*\sqrt{326}=12\sqrt{326}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-216)-12\sqrt{326}}{2*9}=\frac{216-12\sqrt{326}}{18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-216)+12\sqrt{326}}{2*9}=\frac{216+12\sqrt{326}}{18}
$