-2/3y-1/5y=169

Solution for -2/3y-1/5y=169 equation:

-2/3y-1/5y=169

We move all terms to the left:

-2/3y-1/5y-(169)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We calculate fractions


(-10y)/15y^2+(-3y)/15y^2-169=0

We multiply all the terms by the denominator


(-10y)+(-3y)-169*15y^2=0

Wy multiply elements

-2535y^2+(-10y)+(-3y)=0

We get rid of parentheses

-2535y^2-10y-3y=0

We add all the numbers together, and all the variables

-2535y^2-13y=0

a = -2535; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·(-2535)·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*-2535}=\frac{0}{-5070}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*-2535}=\frac{26}{-5070}
=-1/195
$