4+x-1/2x=47

Solution for 4+x-1/2x=47 equation:

4+x-1/2x=47

We move all terms to the left:

4+x-1/2x-(47)=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-43=0

We multiply all the terms by the denominator


x*2x-43*2x-1=0

Wy multiply elements

2x^2-86x-1=0

a = 2; b = -86; c = -1;
Δ = b2-4ac
Δ = -862-4·2·(-1)
Δ = 7404
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:

$\sqrt{\Delta}=\sqrt{7404}=\sqrt{4*1851}=\sqrt{4}*\sqrt{1851}=2\sqrt{1851}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-86)-2\sqrt{1851}}{2*2}=\frac{86-2\sqrt{1851}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-86)+2\sqrt{1851}}{2*2}=\frac{86+2\sqrt{1851}}{4}
$