y-2/9y=42/3

Solution for y-2/9y=42/3 equation:

y-2/9y=42/3

We move all terms to the left:

y-2/9y-(42/3)=0


Domain of the equation: 9y!=0

y!=0/9

y!=0

y∈R


We add all the numbers together, and all the variables

y-2/9y-14=0

We multiply all the terms by the denominator


y*9y-14*9y-2=0

Wy multiply elements

9y^2-126y-2=0

a = 9; b = -126; c = -2;
Δ = b2-4ac
Δ = -1262-4·9·(-2)
Δ = 15948
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:

$\sqrt{\Delta}=\sqrt{15948}=\sqrt{36*443}=\sqrt{36}*\sqrt{443}=6\sqrt{443}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-6\sqrt{443}}{2*9}=\frac{126-6\sqrt{443}}{18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+6\sqrt{443}}{2*9}=\frac{126+6\sqrt{443}}{18}
$