3/7y+11=-1/3y+6

Solution for 3/7y+11=-1/3y+6 equation:

3/7y+11=-1/3y+6

We move all terms to the left:

3/7y+11-(-1/3y+6)=0


Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R



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

y∈R


We get rid of parentheses

3/7y+1/3y-6+11=0

We calculate fractions


9y/21y^2+7y/21y^2-6+11=0

We add all the numbers together, and all the variables

9y/21y^2+7y/21y^2+5=0

We multiply all the terms by the denominator


9y+7y+5*21y^2=0

We add all the numbers together, and all the variables

16y+5*21y^2=0

Wy multiply elements

105y^2+16y=0

a = 105; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·105·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*105}=\frac{-32}{210}
=-16/105
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*105}=\frac{0}{210}
=0
$