-2/5y-1/6y=510

Solution for -2/5y-1/6y=510 equation:

-2/5y-1/6y=510

We move all terms to the left:

-2/5y-1/6y-(510)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We calculate fractions


(-12y)/30y^2+(-5y)/30y^2-510=0

We multiply all the terms by the denominator


(-12y)+(-5y)-510*30y^2=0

Wy multiply elements

-15300y^2+(-12y)+(-5y)=0

We get rid of parentheses

-15300y^2-12y-5y=0

We add all the numbers together, and all the variables

-15300y^2-17y=0

a = -15300; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·(-15300)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*-15300}=\frac{0}{-30600}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*-15300}=\frac{34}{-30600}
=-1/900
$