1/2*y+y=12

Solution for 1/2*y+y=12 equation:

1/2y+y=12

We move all terms to the left:

1/2y+y-(12)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

y+1/2y-12=0

We multiply all the terms by the denominator


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

Wy multiply elements

2y^2-24y+1=0

a = 2; b = -24; c = +1;
Δ = b2-4ac
Δ = -242-4·2·1
Δ = 568
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:

$\sqrt{\Delta}=\sqrt{568}=\sqrt{4*142}=\sqrt{4}*\sqrt{142}=2\sqrt{142}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{142}}{2*2}=\frac{24-2\sqrt{142}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{142}}{2*2}=\frac{24+2\sqrt{142}}{4}
$