y+4/3y-9=1

Solution for y+4/3y-9=1 equation:

y+4/3y-9=1

We move all terms to the left:

y+4/3y-9-(1)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

y+4/3y-10=0

We multiply all the terms by the denominator


y*3y-10*3y+4=0

Wy multiply elements

3y^2-30y+4=0

a = 3; b = -30; c = +4;
Δ = b2-4ac
Δ = -302-4·3·4
Δ = 852
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:

$\sqrt{\Delta}=\sqrt{852}=\sqrt{4*213}=\sqrt{4}*\sqrt{213}=2\sqrt{213}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{213}}{2*3}=\frac{30-2\sqrt{213}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{213}}{2*3}=\frac{30+2\sqrt{213}}{6}
$