4/3*y=-7+1y

Solution for 4/3*y=-7+1y equation:

4/3y=-7+1y

We move all terms to the left:

4/3y-(-7+1y)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

4/3y-(y-7)=0

We get rid of parentheses

4/3y-y+7=0

We multiply all the terms by the denominator


-y*3y+7*3y+4=0

Wy multiply elements

-3y^2+21y+4=0

a = -3; b = 21; c = +4;
Δ = b2-4ac
Δ = 212-4·(-3)·4
Δ = 489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-\sqrt{489}}{2*-3}=\frac{-21-\sqrt{489}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{489}}{2*-3}=\frac{-21+\sqrt{489}}{-6}
$