x+x+1/2x+1/2x=369

Solution for x+x+1/2x+1/2x=369 equation:

x+x+1/2x+1/2x=369

We move all terms to the left:

x+x+1/2x+1/2x-(369)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/2x+1/2x-369=0

We multiply all the terms by the denominator


2x*2x-369*2x+1+1=0

We add all the numbers together, and all the variables

2x*2x-369*2x+2=0

Wy multiply elements

4x^2-738x+2=0

a = 4; b = -738; c = +2;
Δ = b2-4ac
Δ = -7382-4·4·2
Δ = 544612
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:

$\sqrt{\Delta}=\sqrt{544612}=\sqrt{4*136153}=\sqrt{4}*\sqrt{136153}=2\sqrt{136153}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-738)-2\sqrt{136153}}{2*4}=\frac{738-2\sqrt{136153}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-738)+2\sqrt{136153}}{2*4}=\frac{738+2\sqrt{136153}}{8}
$