5y=1/2y-1

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

5y=1/2y-1

We move all terms to the left:

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


Domain of the equation: 2y-1)!=0

y∈R


We get rid of parentheses

5y-1/2y+1=0

We multiply all the terms by the denominator


5y*2y+1*2y-1=0

Wy multiply elements

10y^2+2y-1=0

a = 10; b = 2; c = -1;
Δ = b2-4ac
Δ = 22-4·10·(-1)
Δ = 44
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{11}}{2*10}=\frac{-2-2\sqrt{11}}{20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{11}}{2*10}=\frac{-2+2\sqrt{11}}{20}
$