y=4(2y-8/3)

Solution for y=4(2y-8/3) equation:

y=4(2y-8/3)

We move all terms to the left:

y-(4(2y-8/3))=0

We add all the numbers together, and all the variables

y-(4(+2y-8/3))=0

We multiply all the terms by the denominator


y*3))-(4(+2y-8=0

We add all the numbers together, and all the variables

2y+y*3))-(4(-8=0

Wy multiply elements

3y^2+2y-8=0

a = 3; b = 2; c = -8;
Δ = b2-4ac
Δ = 22-4·3·(-8)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10}{2*3}=\frac{-12}{6}
=-2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10}{2*3}=\frac{8}{6}
=1+1/3
$