4y+3=5/9y+2

Solution for 4y+3=5/9y+2 equation:

4y+3=5/9y+2

We move all terms to the left:

4y+3-(5/9y+2)=0


Domain of the equation: 9y+2)!=0

y∈R


We get rid of parentheses

4y-5/9y-2+3=0

We multiply all the terms by the denominator


4y*9y-2*9y+3*9y-5=0

Wy multiply elements

36y^2-18y+27y-5=0

We add all the numbers together, and all the variables

36y^2+9y-5=0

a = 36; b = 9; c = -5;
Δ = b2-4ac
Δ = 92-4·36·(-5)
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{89}}{2*36}=\frac{-9-3\sqrt{89}}{72}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{89}}{2*36}=\frac{-9+3\sqrt{89}}{72}
$