1/2x+2+x=32

Solution for 1/2x+2+x=32 equation:

1/2x+2+x=32

We move all terms to the left:

1/2x+2+x-(32)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x+1/2x-30=0

We multiply all the terms by the denominator


x*2x-30*2x+1=0

Wy multiply elements

2x^2-60x+1=0

a = 2; b = -60; c = +1;
Δ = b2-4ac
Δ = -602-4·2·1
Δ = 3592
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3592}=\sqrt{4*898}=\sqrt{4}*\sqrt{898}=2\sqrt{898}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{898}}{2*2}=\frac{60-2\sqrt{898}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{898}}{2*2}=\frac{60+2\sqrt{898}}{4}
$