14-2y=6-1/2y

Solution for 14-2y=6-1/2y equation:

14-2y=6-1/2y

We move all terms to the left:

14-2y-(6-1/2y)=0


Domain of the equation: 2y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

-2y-(-1/2y+6)+14=0

We get rid of parentheses

-2y+1/2y-6+14=0

We multiply all the terms by the denominator


-2y*2y-6*2y+14*2y+1=0

Wy multiply elements

-4y^2-12y+28y+1=0

We add all the numbers together, and all the variables

-4y^2+16y+1=0

a = -4; b = 16; c = +1;
Δ = b2-4ac
Δ = 162-4·(-4)·1
Δ = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{17}}{2*-4}=\frac{-16-4\sqrt{17}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{17}}{2*-4}=\frac{-16+4\sqrt{17}}{-8}
$