1/2y+6=2y

Solution for 1/2y+6=2y equation:

1/2y+6=2y

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


-2y*2y+6*2y+1=0

Wy multiply elements

-4y^2+12y+1=0

a = -4; b = 12; c = +1;
Δ = b2-4ac
Δ = 122-4·(-4)·1
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{10}}{2*-4}=\frac{-12-4\sqrt{10}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{10}}{2*-4}=\frac{-12+4\sqrt{10}}{-8}
$