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

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

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

We move all terms to the left:

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


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 2y-6)!=0

y∈R


We get rid of parentheses

-6/5y-1/2y+6-1/5=0

We calculate fractions


(-12y)/250y^2+(-125y)/250y^2+(-2y)/250y^2+6=0

We multiply all the terms by the denominator


(-12y)+(-125y)+(-2y)+6*250y^2=0

Wy multiply elements

1500y^2+(-12y)+(-125y)+(-2y)=0

We get rid of parentheses

1500y^2-12y-125y-2y=0

We add all the numbers together, and all the variables

1500y^2-139y=0

a = 1500; b = -139; c = 0;
Δ = b2-4ac
Δ = -1392-4·1500·0
Δ = 19321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19321}=139$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-139)-139}{2*1500}=\frac{0}{3000}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-139)+139}{2*1500}=\frac{278}{3000}
=139/1500
$