X+3+1/2x+x=48

Solution for X+3+1/2x+x=48 equation:

X+3+1/2X+X=48

We move all terms to the left:

X+3+1/2X+X-(48)=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-45=0

We multiply all the terms by the denominator


2X*2X-45*2X+1=0

Wy multiply elements

4X^2-90X+1=0

a = 4; b = -90; c = +1;
Δ = b2-4ac
Δ = -902-4·4·1
Δ = 8084
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:

$\sqrt{\Delta}=\sqrt{8084}=\sqrt{4*2021}=\sqrt{4}*\sqrt{2021}=2\sqrt{2021}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2021}}{2*4}=\frac{90-2\sqrt{2021}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2021}}{2*4}=\frac{90+2\sqrt{2021}}{8}
$