4y-3/3y=2

Solution for 4y-3/3y=2 equation:

4y-3/3y=2

We move all terms to the left:

4y-3/3y-(2)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We multiply all the terms by the denominator


4y*3y-2*3y-3=0

Wy multiply elements

12y^2-6y-3=0

a = 12; b = -6; c = -3;
Δ = b2-4ac
Δ = -62-4·12·(-3)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{5}}{2*12}=\frac{6-6\sqrt{5}}{24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{5}}{2*12}=\frac{6+6\sqrt{5}}{24}
$