3/4y+8=-1/3y+6

Solution for 3/4y+8=-1/3y+6 equation:

3/4y+8=-1/3y+6

We move all terms to the left:

3/4y+8-(-1/3y+6)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 3y+6)!=0

y∈R


We get rid of parentheses

3/4y+1/3y-6+8=0

We calculate fractions


9y/12y^2+4y/12y^2-6+8=0

We add all the numbers together, and all the variables

9y/12y^2+4y/12y^2+2=0

We multiply all the terms by the denominator


9y+4y+2*12y^2=0

We add all the numbers together, and all the variables

13y+2*12y^2=0

Wy multiply elements

24y^2+13y=0

a = 24; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·24·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*24}=\frac{-26}{48}
=-13/24
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*24}=\frac{0}{48}
=0
$