y-5/9y=36

Solution for y-5/9y=36 equation:

y-5/9y=36

We move all terms to the left:

y-5/9y-(36)=0


Domain of the equation: 9y!=0

y!=0/9

y!=0

y∈R


We multiply all the terms by the denominator


y*9y-36*9y-5=0

Wy multiply elements

9y^2-324y-5=0

a = 9; b = -324; c = -5;
Δ = b2-4ac
Δ = -3242-4·9·(-5)
Δ = 105156
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:

$\sqrt{\Delta}=\sqrt{105156}=\sqrt{36*2921}=\sqrt{36}*\sqrt{2921}=6\sqrt{2921}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-324)-6\sqrt{2921}}{2*9}=\frac{324-6\sqrt{2921}}{18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-324)+6\sqrt{2921}}{2*9}=\frac{324+6\sqrt{2921}}{18}
$