-2(5y-1)-y=-4/y-3

Solution for -2(5y-1)-y=-4/y-3 equation:

-2(5y-1)-y=-4/y-3

We move all terms to the left:

-2(5y-1)-y-(-4/y-3)=0


Domain of the equation: y-3)!=0

y∈R


We add all the numbers together, and all the variables

-1y-2(5y-1)-(-4/y-3)=0

We multiply parentheses

-1y-10y-(-4/y-3)+2=0

We get rid of parentheses

-1y-10y+4/y+3+2=0

We multiply all the terms by the denominator


-1y*y-10y*y+3*y+2*y+4=0

We add all the numbers together, and all the variables

5y-1y*y-10y*y+4=0

Wy multiply elements

-1y^2-10y^2+5y+4=0

We add all the numbers together, and all the variables

-11y^2+5y+4=0

a = -11; b = 5; c = +4;
Δ = b2-4ac
Δ = 52-4·(-11)·4
Δ = 201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{201}}{2*-11}=\frac{-5-\sqrt{201}}{-22}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{201}}{2*-11}=\frac{-5+\sqrt{201}}{-22}
$