1/2x+x=4.8

Solution for 1/2x+x=4.8 equation:

1/2x+x=4.8

We move all terms to the left:

1/2x+x-(4.8)=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-4.8=0

We multiply all the terms by the denominator


x*2x-(4.8)*2x+1=0

We multiply parentheses

x*2x-9.6x+1=0

Wy multiply elements

2x^2-9.6x+1=0

a = 2; b = -9.6; c = +1;
Δ = b2-4ac
Δ = -9.62-4·2·1
Δ = 84.16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9.6)-\sqrt{84.16}}{2*2}=\frac{9.6-\sqrt{84.16}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9.6)+\sqrt{84.16}}{2*2}=\frac{9.6+\sqrt{84.16}}{4}
$