2/9y+45=6y

Solution for 2/9y+45=6y equation:

2/9y+45=6y

We move all terms to the left:

2/9y+45-(6y)=0


Domain of the equation: 9y!=0

y!=0/9

y!=0

y∈R


We add all the numbers together, and all the variables

-6y+2/9y+45=0

We multiply all the terms by the denominator


-6y*9y+45*9y+2=0

Wy multiply elements

-54y^2+405y+2=0

a = -54; b = 405; c = +2;
Δ = b2-4ac
Δ = 4052-4·(-54)·2
Δ = 164457
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:

$\sqrt{\Delta}=\sqrt{164457}=\sqrt{9*18273}=\sqrt{9}*\sqrt{18273}=3\sqrt{18273}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(405)-3\sqrt{18273}}{2*-54}=\frac{-405-3\sqrt{18273}}{-108}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(405)+3\sqrt{18273}}{2*-54}=\frac{-405+3\sqrt{18273}}{-108}
$