-6=1/5y-y-1

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

-6=1/5y-y-1

We move all terms to the left:

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


Domain of the equation: 5y-y-1)!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


1y*5y+1*5y-6*5y-1=0

Wy multiply elements

5y^2+5y-30y-1=0

We add all the numbers together, and all the variables

5y^2-25y-1=0

a = 5; b = -25; c = -1;
Δ = b2-4ac
Δ = -252-4·5·(-1)
Δ = 645
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{-(-25)-\sqrt{645}}{2*5}=\frac{25-\sqrt{645}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{645}}{2*5}=\frac{25+\sqrt{645}}{10}
$