X+4+1/2x+x-4=46

Solution for X+4+1/2x+x-4=46 equation:

X+4+1/2X+X-4=46

We move all terms to the left:

X+4+1/2X+X-4-(46)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We add all the numbers together, and all the variables

2X+1/2X-46=0

We multiply all the terms by the denominator


2X*2X-46*2X+1=0

Wy multiply elements

4X^2-92X+1=0

a = 4; b = -92; c = +1;
Δ = b2-4ac
Δ = -922-4·4·1
Δ = 8448
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:

$\sqrt{\Delta}=\sqrt{8448}=\sqrt{256*33}=\sqrt{256}*\sqrt{33}=16\sqrt{33}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-92)-16\sqrt{33}}{2*4}=\frac{92-16\sqrt{33}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-92)+16\sqrt{33}}{2*4}=\frac{92+16\sqrt{33}}{8}
$