9/10y+2/7y=-6/5

Solution for 9/10y+2/7y=-6/5 equation:

9/10y+2/7y=-6/5

We move all terms to the left:

9/10y+2/7y-(-6/5)=0


Domain of the equation: 10y!=0

y!=0/10

y!=0

y∈R



Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R


We get rid of parentheses

9/10y+2/7y+6/5=0

We calculate fractions


2940y^2/1750y^2+1575y/1750y^2+500y/1750y^2=0

We multiply all the terms by the denominator


2940y^2+1575y+500y=0

We add all the numbers together, and all the variables

2940y^2+2075y=0

a = 2940; b = 2075; c = 0;
Δ = b2-4ac
Δ = 20752-4·2940·0
Δ = 4305625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4305625}=2075$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2075)-2075}{2*2940}=\frac{-4150}{5880}
=-415/588
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2075)+2075}{2*2940}=\frac{0}{5880}
=0
$