(1/6)*y=5*y+9

Solution for (1/6)*y=5*y+9 equation:

(1/6)*y=5y+9

We move all terms to the left:

(1/6)*y-(5y+9)=0


Domain of the equation: 6)*y!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

(+1/6)*y-(5y+9)=0

We multiply parentheses

y^2-(5y+9)=0

We get rid of parentheses

y^2-5y-9=0

a = 1; b = -5; c = -9;
Δ = b2-4ac
Δ = -52-4·1·(-9)
Δ = 61
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{61}}{2*1}=\frac{5-\sqrt{61}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{61}}{2*1}=\frac{5+\sqrt{61}}{2}
$