1/2x+x=670

Solution for 1/2x+x=670 equation:

1/2x+x=670

We move all terms to the left:

1/2x+x-(670)=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-670=0

We multiply all the terms by the denominator


x*2x-670*2x+1=0

Wy multiply elements

2x^2-1340x+1=0

a = 2; b = -1340; c = +1;
Δ = b2-4ac
Δ = -13402-4·2·1
Δ = 1795592
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:

$\sqrt{\Delta}=\sqrt{1795592}=\sqrt{4*448898}=\sqrt{4}*\sqrt{448898}=2\sqrt{448898}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1340)-2\sqrt{448898}}{2*2}=\frac{1340-2\sqrt{448898}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1340)+2\sqrt{448898}}{2*2}=\frac{1340+2\sqrt{448898}}{4}
$