2/3y+8=2y

Solution for 2/3y+8=2y equation:

2/3y+8=2y

We move all terms to the left:

2/3y+8-(2y)=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+2/3y+8=0

We multiply all the terms by the denominator


-2y*3y+8*3y+2=0

Wy multiply elements

-6y^2+24y+2=0

a = -6; b = 24; c = +2;
Δ = b2-4ac
Δ = 242-4·(-6)·2
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{39}}{2*-6}=\frac{-24-4\sqrt{39}}{-12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{39}}{2*-6}=\frac{-24+4\sqrt{39}}{-12}
$