1/2x+x=1920

Solution for 1/2x+x=1920 equation:

1/2x+x=1920

We move all terms to the left:

1/2x+x-(1920)=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-1920=0

We multiply all the terms by the denominator


x*2x-1920*2x+1=0

Wy multiply elements

2x^2-3840x+1=0

a = 2; b = -3840; c = +1;
Δ = b2-4ac
Δ = -38402-4·2·1
Δ = 14745592
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:

$\sqrt{\Delta}=\sqrt{14745592}=\sqrt{4*3686398}=\sqrt{4}*\sqrt{3686398}=2\sqrt{3686398}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3840)-2\sqrt{3686398}}{2*2}=\frac{3840-2\sqrt{3686398}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3840)+2\sqrt{3686398}}{2*2}=\frac{3840+2\sqrt{3686398}}{4}
$