1/2x+x=48

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

1/2x+x=48

We move all terms to the left:

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

x+1/2x-48=0

We multiply all the terms by the denominator


x*2x-48*2x+1=0

Wy multiply elements

2x^2-96x+1=0

a = 2; b = -96; c = +1;
Δ = b2-4ac
Δ = -962-4·2·1
Δ = 9208
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:

$\sqrt{\Delta}=\sqrt{9208}=\sqrt{4*2302}=\sqrt{4}*\sqrt{2302}=2\sqrt{2302}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-2\sqrt{2302}}{2*2}=\frac{96-2\sqrt{2302}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+2\sqrt{2302}}{2*2}=\frac{96+2\sqrt{2302}}{4}
$