1/2y-y=6

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

1/2y-y=6

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -2; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·(-2)·1
Δ = 152
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:

$\sqrt{\Delta}=\sqrt{152}=\sqrt{4*38}=\sqrt{4}*\sqrt{38}=2\sqrt{38}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{38}}{2*-2}=\frac{12-2\sqrt{38}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{38}}{2*-2}=\frac{12+2\sqrt{38}}{-4}
$