5y+2=2y+1/2y

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

5y+2=2y+1/2y

We move all terms to the left:

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


Domain of the equation: 2y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

6y^2+4y-1=0

a = 6; b = 4; c = -1;
Δ = b2-4ac
Δ = 42-4·6·(-1)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{10}}{2*6}=\frac{-4-2\sqrt{10}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{10}}{2*6}=\frac{-4+2\sqrt{10}}{12}
$