5y-6=4/3y+6

Solution for 5y-6=4/3y+6 equation:

5y-6=4/3y+6

We move all terms to the left:

5y-6-(4/3y+6)=0


Domain of the equation: 3y+6)!=0

y∈R


We get rid of parentheses

5y-4/3y-6-6=0

We multiply all the terms by the denominator


5y*3y-6*3y-6*3y-4=0

Wy multiply elements

15y^2-18y-18y-4=0

We add all the numbers together, and all the variables

15y^2-36y-4=0

a = 15; b = -36; c = -4;
Δ = b2-4ac
Δ = -362-4·15·(-4)
Δ = 1536
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:

$\sqrt{\Delta}=\sqrt{1536}=\sqrt{256*6}=\sqrt{256}*\sqrt{6}=16\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-16\sqrt{6}}{2*15}=\frac{36-16\sqrt{6}}{30}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+16\sqrt{6}}{2*15}=\frac{36+16\sqrt{6}}{30}
$