1/2y=32/2-7y

Solution for 1/2y=32/2-7y equation:

1/2y=32/2-7y

We move all terms to the left:

1/2y-(32/2-7y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 2-7y)!=0

We move all terms containing y to the left, all other terms to the right

-7y)!=-2

y!=-2/1

y!=-2

y∈R


We add all the numbers together, and all the variables

1/2y-(-7y+16)=0

We get rid of parentheses

1/2y+7y-16=0

We multiply all the terms by the denominator


7y*2y-16*2y+1=0

Wy multiply elements

14y^2-32y+1=0

a = 14; b = -32; c = +1;
Δ = b2-4ac
Δ = -322-4·14·1
Δ = 968
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:

$\sqrt{\Delta}=\sqrt{968}=\sqrt{484*2}=\sqrt{484}*\sqrt{2}=22\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-22\sqrt{2}}{2*14}=\frac{32-22\sqrt{2}}{28}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+22\sqrt{2}}{2*14}=\frac{32+22\sqrt{2}}{28}
$