-5y+7/3y=-5-8/3y-4

Solution for -5y+7/3y=-5-8/3y-4 equation:

-5y+7/3y=-5-8/3y-4

We move all terms to the left:

-5y+7/3y-(-5-8/3y-4)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 3y-4)!=0

y∈R


We add all the numbers together, and all the variables

-5y+7/3y-(-8/3y-9)=0

We get rid of parentheses

-5y+7/3y+8/3y+9=0

We multiply all the terms by the denominator


-5y*3y+9*3y+7+8=0

We add all the numbers together, and all the variables

-5y*3y+9*3y+15=0

Wy multiply elements

-15y^2+27y+15=0

a = -15; b = 27; c = +15;
Δ = b2-4ac
Δ = 272-4·(-15)·15
Δ = 1629
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:

$\sqrt{\Delta}=\sqrt{1629}=\sqrt{9*181}=\sqrt{9}*\sqrt{181}=3\sqrt{181}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{181}}{2*-15}=\frac{-27-3\sqrt{181}}{-30}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{181}}{2*-15}=\frac{-27+3\sqrt{181}}{-30}
$