1/2y+y=4

Solution for 1/2y+y=4 equation:

1/2y+y=4

We move all terms to the left:

1/2y+y-(4)=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-4=0

We multiply all the terms by the denominator


y*2y-4*2y+1=0

Wy multiply elements

2y^2-8y+1=0

a = 2; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·2·1
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{14}}{2*2}=\frac{8-2\sqrt{14}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{14}}{2*2}=\frac{8+2\sqrt{14}}{4}
$