x+2x+1/2x=1260

Solution for x+2x+1/2x=1260 equation:

x+2x+1/2x=1260

We move all terms to the left:

x+2x+1/2x-(1260)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x+1/2x-1260=0

We multiply all the terms by the denominator


3x*2x-1260*2x+1=0

Wy multiply elements

6x^2-2520x+1=0

a = 6; b = -2520; c = +1;
Δ = b2-4ac
Δ = -25202-4·6·1
Δ = 6350376
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:

$\sqrt{\Delta}=\sqrt{6350376}=\sqrt{4*1587594}=\sqrt{4}*\sqrt{1587594}=2\sqrt{1587594}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2520)-2\sqrt{1587594}}{2*6}=\frac{2520-2\sqrt{1587594}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2520)+2\sqrt{1587594}}{2*6}=\frac{2520+2\sqrt{1587594}}{12}
$