(5y+2)-(16/3y+1)=8

Solution for (5y+2)-(16/3y+1)=8 equation:

(5y+2)-(16/3y+1)=8

We move all terms to the left:

(5y+2)-(16/3y+1)-(8)=0


Domain of the equation: 3y+1)!=0

y∈R


We get rid of parentheses

5y-16/3y+2-1-8=0

We multiply all the terms by the denominator


5y*3y+2*3y-1*3y-8*3y-16=0

Wy multiply elements

15y^2+6y-3y-24y-16=0

We add all the numbers together, and all the variables

15y^2-21y-16=0

a = 15; b = -21; c = -16;
Δ = b2-4ac
Δ = -212-4·15·(-16)
Δ = 1401
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{1401}}{2*15}=\frac{21-\sqrt{1401}}{30}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{1401}}{2*15}=\frac{21+\sqrt{1401}}{30}
$