4/3y+2y=30

Solution for 4/3y+2y=30 equation:

4/3y+2y=30

We move all terms to the left:

4/3y+2y-(30)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

2y+4/3y-30=0

We multiply all the terms by the denominator


2y*3y-30*3y+4=0

Wy multiply elements

6y^2-90y+4=0

a = 6; b = -90; c = +4;
Δ = b2-4ac
Δ = -902-4·6·4
Δ = 8004
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:

$\sqrt{\Delta}=\sqrt{8004}=\sqrt{4*2001}=\sqrt{4}*\sqrt{2001}=2\sqrt{2001}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2001}}{2*6}=\frac{90-2\sqrt{2001}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2001}}{2*6}=\frac{90+2\sqrt{2001}}{12}
$